I'll be taking my daughter to NYC over Memorial Day weekend. So far, this is our plan:
Saturday: arriving at around noon at Penn Station, take cab to the hotel (Sheraton Manhattan--- their deal was too good to pass up), drop off luggage, walk down to the Empire State Building, checking out some stores on the way. Get back to hotel, check in. Take a sunset boatride on circle line.

Sunday:
A museum and/or flea market
central park? Greenwich?
Beauty and the Beast at 6:30 p.m.
Which flea markets are there on Sundays? And are many stores closed?

Monday?
Museum and ?

We'll be leaving 6:30 from Penn Station

Also, I still need suggestions for restaurant, either around Pier 81 (or wherever Circle Line leaves) and for restaurant for quick bite after show (Sunday). Do I need reservations?

Thanks a lot!

As a mom of a kid near your daughter's age, after your sunset cruise, you MUST head into Times Square and see it all lit up and dazzling. There are usually shuttle buses from the cruise sites right to 42nd Street in the middle of Times Square. Your daughter will be thrilled. There's a HUGE Toys R Us on a prominent corner with a ferris wheel INSIDE. Please don't pass this up!

One more thing. If you're starving, you can buy hot dogs and such on the boat. Don't eat around the pier, there are lots of kid-friendly places in Times Square if you're still hungry.

Your daughter might like Canal street--kind of a flea market atmosphere with haggling over prices on knock-off accessories. If you go to the Metropolitan Musuem make sure you go up to the roof garden. on Sunday stores have limited hours,12-6, but most are open.
Circle Line leaves from one of 2 piers--which tour are you taking? Where you eat will depend on that. Check out www.zagat.com for some ideas--there are too many places to list.

Museums are all closed on Monday. I would try Serendipity for lunch. A 10 year old girl's dream. Ruby Foo after the show should be good for a 10 year old too, or Planet Hollywood (food is eh, but kids love it). Walk around china town & little italy. Central Park is great too.

For Sunday, you can hit the flea market on Columbus Avenue at 77th street. It's in a schoolyard, (and inside the building, but you probably won't bother going inside). It's also across the street from the Museum of Natural History and Rose Space center which you must see. Admission is officially "pay as you wish" so don't feel like you have to spend the suggested $10 per person if you just want to hop in and look around.
The space show itself is a set fee (and because it 'includes' the suggested fee, it's a steep $19 --but you'll have fun just looking around for half an hour to an hour).
Lot's of places to eat nearby (pizza, chinese, diners, fancier brunch places--need suggestions?).Many are usually crowded, but New Yorkers are generally going to be out of town that weekend so it will be quieter than usual.
At this point, you're across the street from one of the main entrances to Central Park.
A nice easy walk is in at the 81st street entrance, walking straight across to the middle of the park's "Great Lawn"
where you'll also see Belvedere Castle (now a station of the weather service), The Delacorte Theater (where there are free shows later in the summer), the lake, model boat ponds, and just about every kind of street musician (although there are an awful lot of people playing Beatles tunes on any given day). If you keep going straight across the park you'll end up at the Metropolitan Museum of Art. If you take your daughter to one museum, this has to be it (BTW--most NYC museums are closed Mondays--only Natural History [and Museum of Modern Art--which will probably be closed for renovations by then} are open)
Favorite spots at the Met are the costume collection (see if there's an exhibit on when you're there), The egyptian Temple of Dendur, indoor Asian gardens, and various period rooms (and oh, yeah, one of the world's finest collections of paintings). This museum is also pay as you wish, so don't feel obligated to cough up the full amount if you can't and or don't want to shell out
so much for a short visit.
You can actually reverse this whole itinerary at start at the Met (opens at 9:30) if you want...
It's easy to get back to the hotel to rest or straight to the show from either side of the park

Thanks for the great advice so far and for pointing out that the Metropolitan Museum is closed on Mondays (don't know what I was copying in my notebook). The Guggenheim, however, is open on Mondays.

The two-hour sunset boat ride leaves at 7 p.m. from Pier 83, 42nd West/12th Street; so we should either eat before near the pier or somewhere on the way from the Sheraton to the pier.

Assuming we'll follow Janie's advice above for Sunday, what should we do on Monday? Of course, much of our itinerary will depend on the weather, plus I don't want to pack our schedule too much.

It's Navy Fleet Week from May 22-28 so there will be ships to tour if you think that would interest her. There will be plenty of female sailors and that would certainly be a learning experience!

Sounds like a great weekend! So Saturday you'll be in midtown, Sunday might be Upper West Side-Central Park-Met. So Monday should probably be a look downtown - as Ellen suggested Chinatown and Little Italy and if you're still going strong, window shopping in Soho.

If it's crummy weather...hmm - ice skating or bowling at Chelsea Piers (if they're open that Monday), or an Imax movie at Loews Cineplex Lincoln Square? (Right now there's Space Station 3D which sounds great - it shows life on the space station - or Beauty and the Beast )

As for restaurants, in midtown there are the usual recommendations which are great - the previously mentioned Ruby Foo's, John's Pizzeria or Virgil's (BBQ). Or walk down Ninth Ave and stop in at a place that appeals to you both. There's Vynl at 54th St & Eatery at 53rd St down to the Film Center Cafe at 45th & Zuni at 43rd with a whole bunch of good places in between. Delta Grill at 48th St is Cajun/Creole and Kodama on 45th St between 9th Ave & 8th Ave is Japanese.

Any suggestions for Little Italy, Chinatown, Greenwich Village re. what to do, where to eat? Also, what is South Street Seaport like?

To me, South Street Seaport is just a mall but I'm not a nautical lover. There are usually a couple of old ships you can explore and a museum which is closed for renovations currently. Despite my non-love of the place I think we'll be going there soon because you can ride the Beast there and my child really wants to do this. The Beast is a large motorboat and although you can also ride it on the Hudson, from South St Seaport it supposedly cruises by the Statue of Liberty and goes under the Brooklyn Bridge.

Regarding Chinatown/Little Italy, there are a lot of posts about where to eat ("Best Chinese Restaurants", "Joe's Shanghai Chinatown...", "Dim Sum in NYC?" and "Where to eat in Little Italy" among others). An interesting drink you can try is "bubble tea". There are lots of Hong Kong, modern looking coffee shops around (try Mott St, Mulberry St, Bayard) which sell it - it's cold, flavored tea with dark tapioca balls at the bottom and the straw is extra large to accommodate the "bubbles".

I would just walk around, especially taking the smaller side streets - Mosco, Pell, etc. I like going into Kam Man Market on Canal & Mulberry for interesting food products. For Little Italy, walk up Mulberry from Canal up to Houston, looking for a place to have gelato or pastries.

Soho is to the west of Little Italy. Greenwich Village is further north and may be a separate trip, depending on your stamina.

You can start at Washington Square Park. If you go north to 8th St, then east you'll go past Astor Place then 8th St changes names to St. Mark's Place. Walk along funky St. Mark's to explore the East Village. If you go that way, you can eat at Miracle Grill on First Ave between 6th & 7th Sts - Southwestern with a garden in back. Or Two Boots Restaurant on Ave A between 2nd & 3rd (They also have a pizzeria one block north.)

Or from Washington Square go south to Bleecker, then west. The original John's Pizzeria is between Sixth & Seventh Ave. I like walking the small streets in the West Village - Carmine, Morton, Bedford, Barrow, Grove St where there's Miss Majesty's Lollipop Playhouse (young children's plays - your 10-year-old is probably too old). If you don't eat at John's, you can try the Cowgirl Hall of Fame on Hudson & 10th St - Tex Mex food I guess you'd call it. The streets are really crazy in the West Village (my personal opinion - I invariably get lost or get all turned around) so consult a map - or it might be fun to get lost.

The Forbes Gallery north of Washington Square Park on Fifth Ave at 12th St is interesting. It has Faberge eggs & antique toys, but they're closed on Sundays & Mondays.

Thanks for the info; I think we'll skip South Street since neither mem nor my daughter are too interested in ships and will head for Chinatown since that's something she's never seen. I think we'll just play it by ear.
And once my search function works again, I'll do the searches you suggested.