A couple of notes:

Yes, I would grab a cab from JFK to you hotel. The cost will be about $60 - $45 flat fare plus toll and 20% tip.

The SoL is closed for renovations - so you can only spend a small amount of time looking at the outside. The ferry goes on to the Ellis Island Immigration Museum and I would see that - it's brilliant. About 9 is right since there is a security line (think airline type security -no large bags) to get on the ferry.

On Friday I wold do Top of the Rock since youare in the general area. Go up around dusk - so you can see the city both in daylight and lit up at night.

For dinners I would get away from Time Square - where food is often either 1) overprices or 2) chain places with the same ghsatly micro-nuked stuff you can get at the mall - but at twice hte price. I would explore a differnt neighborhood each evenng and try to stick to sidewalk cafes where possible - so you have the interst of people waatching as well as dinner. Go to the Village, the Est Village, SoHo/helsea, the upper west side, etc. There are hundreds of sidewalk cafes (menupages.com will help you find places of the ethnicitie yuowant - or places that have gluten free items).

With 4 people and luggage I would get a car service to EWR (try Dial 7 - look at the web site for discount coupons) - but plan on abuot $85/$90.

I would NOT take a celebrity tour. All you see is the outside of a lot of buildings where people have or had lived. Instead when you get here call 311 and ask them for the web site that tells you waht movies and TV shows are currently being shot here (there is almost always something). Then you can spend an hour or two there and perhaps see alive celeb.

Cannot comprehend going to Hoboken for a bakery!

Definitely do Met and AMNH - but look at web sites tosee what departments you want - since either one can take days to cover.

Good news the garbage strike is over.

Here is a list of many cheap ways to eat that I have posted before.

How to eat cheaply in NYC

Breakfast

Every, and I do mean every, neighborhood in Manhattan has what are euphemistically called delis. Almost all have some sort of breakfast specials that usually includes eggs, potatoes, toast and coffee. If you are not hungry or are cholesterol adverse, they also usually sell sliced fruit and yogurt. Of course there are bagels and pastries. NEVER EVER order room service.

There are many places that make their bagels. NOT DUNKIN DONUS. Some of the better one’s include Ess-a-Bagel,. Murray’s Tal’s, David’s.

Lunch

Part of the NY experience is to avoid chain restaurants. There is an incredible variety of inexpensive foods, among them Chinese and Indian. Quality varies substantially. If you are in or near Chinatown, there are many places including Big Wong’s. If you are near the East Village East 6th Street has literally 14 Indian restaurants to choose from. There are also excellent Indian restaurants on Lexington Avenue in the 20’s. The East Village also offers inexpensive Eastern European cooking at Veselka comfort food at Mama’s.

No NY’er cannot resist a frank at Gray’s Papaya who also sells fruit drinks including papaya, hence the name. There are now many variations on papaya and dogs all are inexpensive. I do not think the fruit drinks have ever come in contact with real fruit, but that also is part of the charm. Nathan’s are also very good but they are more expensive.

Pizza is a long lunch standby-do not go to ANY chain, the cheese is older than the kids who make it. Look for by the slice places and try a calzone as well, you will not eat for two days.

Sidewalk hot dog venders are always cheap, avoid the guys around Rock Center, you pay a premium. There are those who wonder about the hygiene, the dogs are boiled and the knishes grilled for forever. It must kill anything that lurks

Free samples are available at Dean & Deluca, Sarabeth’s, and Gourmet Garage.

It is the rare independent bakery in NYC that does not have at least one bread or pastry that is enticing.

With the economy is bad many restaurants are offering Recession specials, so keep your eye out., especially pizza places and the Indian places on 6th Street

The following are inexpensive meals and desserts:

Inexpensive Italian- La Marca (3rd Ave. and 22 Street, only opened noon-10 PM, Mon-Fri), Excellent Food Value

Inexpensive Eastern European- Veselka,

Dessert-Veniero's, DeRobertis for the frozen lemon thing and cannoli , Fat Witch Bakery (brownies only) Chelsea Market

Brunches-, I Coppi, (best $15 brunch we have had in a long time) Turkish Kitchen, Cafecito (Ave C), Clinton Street Bakery, City Bakery

Pizza-Motorino, they luncheon special with individual pizza is a great great buy, also Lombardi’s

Hole in the wall-Stage (next to Stomp) great cheap home made soups

French fires-Pomme Frites

Inexpensive American-Mama’s

Ice Cream-Cones on Bleecker, Il Laboratorio de Gelato, Chinatown Ice Cream Factory, Cones and Sundae (East 10th off Third) Ronnybrook at the Chelsea market

Chinatown-Big Wong. Joe’s Ginger, NY Noodletown

Dim Sum-Jing Fung, Golden Unicorn, Nom Wah on Doyers Street

Sandwiches-Dafonte-the meatball tastes like old Brooklyn and where else can still get potato and egg sandwiches.

Tapas-Despana on Broome Street, Nai

Inexpensive French Bistro-Sans Coulette

We recently returnefd from 18 days in NYC, located at the border between Chelsea and Greenwich Village.

I would recommend The Highline, probably walking in the southern direction starting at West 30th Street. It is most interesting.

We also took the (free) Staten Island Ferry. It leaves every half-hour (more frequently during prime commuting times), and you can join the throngs of visitors who immediately return to Manhattan on the next ferry. The views of Manhattan while returning cannot be beat.

Your hotel is two blocks south of Times Square "proper" - and thus a relief to not be in the middle of the crush. (I happened to walk by it just a few hours ago on my way home - little did I know!) It's very close to the bucolic Bryant Park, which in addition to being a lovely square of green in the middle of midtown, has a number of kiosks selling good-quality takeaway eats and coffee. The Bryant Park Grill at the eastern side of the space is a good for a nice meal "al fresco".
bryantpark.org

Along the south side of the park, on 40th Street between 6th and 5th Avenues, there is a Pain Quotidien (one of a chain of delicious Belgian cafes). Your poor son won't get to taste the gluten stuff, but they have lots else to offer. A little farther east on that block, there is a nice gourmet grocery called Zeytinz.
www.lepainquotidien.com
www.zeytinz.com

To go up to the Met, you may well want to walk from your hotel to Grand Central (take a tour if you have time/inclination - it's a great space!), cutting through Bryant Park and past the front of the New York Public Library with its lions as you go.

If you are heading to Grand Central, you could pass by the short, mostly nondescript block of 41st Street between 5th and Madison Avenues, notable as having 3 Japanese takeout shops along the south side of the street: an outpost of the locally-famous Sunrise Mart; my fave Cafe Zaiya, and another one. (Cafe Zaiya also has a pretty eatery in the large Japanese bookstore Kinokuniya on 6th Ave at 41st Street, overlooking Bryant Park.)
http://zaiyany.com

The "basement" level of Grand Central is the dining concourse, where there are counter-sized outposts of a number of well-known NYC restaurants. On the main level, there are a number of good shops (I love the cute trinkets at Pylones!), takeaway coffee/wine/beer, etc. See the lists on this website: www.grandcentralterminal.com

...And I almost forgot to add what I was going to say initially-! The area west of Times Square along 9th Ave from about 42-57th Street is much better for dining options than the "main" part of Times Square. (This is the neighborhood called Clinton by marketers and Hells Kitchen by locals.) A lot of good, inexpensive Thai - look for any of the Wondee Siam and Yum Yum locations, and my fave Pams Real Thai - plus Brazilian, Greek, diners, etc. The restaurant Vynl Diner is a higher-end diner with Asian-inspired options and a funky decor. I'd also recommend tiny Island Burgers and Shakes (chicken too) - you could always order sans bun-! (Sadly, both Vynl and IBnS have awesome shakes. Don't tell your kids!)

In NYC, a great dining resource is menupages.com - locations, hours, sample menus, user reviews, etc. Plug in the names of any of these places and see what you like!

The Met museum is a must!! Find out what the kids have recently studied in school and then go look at stuff that relates. They may have read about it or googled it but at the Met they will see the real thing. Check out the website.

Here's a gluten-free restaurant in the village http://risotteria.com/

And here's a very good chinese restaurant just around the block from your hotel http://szechuangourmetnyc.com/food-delivery-TW/szechuan-gourmet-new-york-city.3764.r?QueryStringValue=jVvEmfB+e+3VSgkJ5CYg2Q==

Note when they say Szechuan they mean Szechuan. Pay attention to those little peppers on the menu if someone doesn't like spicy foods.

In the East Village, you might check out Tu-Lu's gluten-free bakery or on the Lower East Side go to Babycakes for dairy free gluten-free items. Might be a special treat for your son.

Stay away from Le Pain quotidian. I am gluten-free and have a friend who only likes to eat there (don't ask) I feel like the only thing there I can eat is yogurt, and that doesn't work if your son is Dairy-free.

There's a pretty good gluten-free chinese restaurant near Bloomingdales, will think if I can figure out the name of it.

Would you consider splitting up for the day your daughter wants to go to NJ to the Cake Boss store? Maybe your husband and son could do something special that day considering your son won't be able to eat anything from the Cake Boss bakery.

Oh and I just read in the New York Times about another gluten-free bakery that opened up on the UES. It was a week or two ago in the dining section.

Regarding your daughter's wish to see celebrities: I think the most likely part of NYC for that would be SoHo or Tribeca. Maybe the West Village.

You might be interested in this thread for a woman who wants to go shopping with her 14-year-old daughter. I outlined some shops they could visit between Canal and Houston Streets in Soho, and others had suggestions in other areas of the city:
http://www.fodors.com/community/united-states/new-york-with-14yr-old-girl.cfm?13

On your day in the Financial District, look into doing a walking tour there. (IMHO, much more interesting than Soho/Chinatown-!) The layers of history at the tip of Manhattan are so much richer and more varied than any other part of the city.

While downtown, you might want to check out the New Amsterdam Market, a recent addition to the open-air market scene; Sundays only just south of the Brooklyn Bridge and north of South Street Seaport. www.newamsterdammarket.org

Alternately, you could walk up to City Hall Park and then over (all or part) of the Brooklyn Bridge. (If you walk the whole way, you could venture into the adjacent Dumbo or Brooklyn Heights neighborhoods, or just hop the A/C subway nearby; the next stop Manhattan-bound is Fulton Street, putting you right back at "ground zero" for your memorial visit.)

Century 21 is an NYC discount-shopping institution. Its flagship location right across from "ground zero" is great (dangerous?) for killing some time; go to the upper floors for a little more breathing space from the crowds of shoppers...

If you like Indian food, the tiny, casual Ruchi on the edge of "ground zero" has terrific food in an unassuming space:
www.menupages.com/restaurants/ruchi

Oh, and on your theater evenings, I thought of another place for dinner, a little closer than 9th Ave (though you'll be fine pre-theater at any of those places). Pongsri is a good Thai restaurant, nicer than the casual places I mentioned on 9th Ave. It's on W 48th Street just east of 8th Ave. http://pongsri.com - look for Theater District location

// There are a ton of street markets, open-air and otherwise, in the city at this time of year.
- Here's some coverage from NYC's tourism bureau from last year; all the ones listed that I know are still going strong this year: www.nycgo.com/slideshows/nyc-flea-markets-2011
- This site lists some long-running flea markets and street fairs, and includes a link to a calendar of events: www.nyctourist.com/shopping/flea_markets.php
- New York Magazine has a great section on shopping. Click on "show all" under Types & Features on the left side for a link to a list of Fairs and Fleas: http://nymag.com/shopping

// There was recently a trip report on here by someone who had visited NYC and seen a lot of celebrities; the word "celebrities" was in the title. She included a link to a site for finding out where film shootings, etc., are each day (similar to calling 311 as nytraveler suggests).

Thanks for all the advice!

- Perfect idea! I am checking menupages for ideas on where to eat. Great site!
- Thanks for the restaurant reccomendations!
- We really want to avoid chain food restaurants!
- Awesome idea on splitting up for the American Museum and Cake Boss bakery. Everyone is now happy!
- Thanks for the advice on going past the library on the way to Grand Central!
- Oh my gosh - thanks so much for the mention of the Japanese bookstore - my son will love that!!! He love books and has a thing for Japanese (he's taking a Japanese language class)
- Chinese around the corner sounds wonderful for a quick bite!
- Thank so much for the gluten free recommendations! Also I had no idea that Babycakes had dairy/gluten free items. Yum!
- Wow - discount stores - perfect! Thanks for the link to shopping thread and the street markets!

So much thanks to everyone! I feel so much better now! I really feel like I might know what I am doing! You are all so wonderful !!

So glad to hear it!!

My Japanofile friends love Kinokuniya. If I remember correctly, they carry all sorts of Japanese paper, pens, etc. in addition to the books. These same friends have brought us authentic sweets from the Japanese bakery at Rockefeller Center:
http://www.yelp.com/biz/minamoto-kitchoan-new-york

Since your son has a thing for Japanese (and not to squeeze more into your trip!), maybe there's a program that interests him at the Japan Society:
http://www.japansociety.org/

...But you'll find more than enough things Japanese in midtown to fill an entire trip.

For your daughter, in case you hadn't found it, here's the recent celebrity-filled trip report I mentioned:
http://www.fodors.com/community/united-states/celebrities-sightings-in-nyc.cfm

Here's a popular Italian restaurant with great food that specializes in gluten-free: Bistango (corner of 29th/3rd Avenue). Tell them in advance, and I'm sure they can do a dairy-free meal as well. This is a neighborhood restaurant, but a popular one. Make a reservation at least a day ahead for 4 if you want to eat at a specific time (even on a weekday). Telephone: (212) 725-8484.

There aren't many tourist attractions nearby, so I'm not sure you'll want to do this as a special-trip restaurant, but it's a good choice if you do.