What kinds of food would they like -- burgers? Mexican? Sushi?

I would say all-American fare,Italian,Mexican...for one picky eater, Chinese is out unfortunately

assuming sushi would be out as well :/

If you want "all-American" you're very unlikely to find a trendy place.

The Breslin might do, but it's in the Ace Hotel in northern Chelsea, not in the Village. It's from the same owners as The Spotted Pig, which is in the Village. Both these are British gastro-pubs, but I think the cuisine will fit with your picky girls, and they can always get burgers there.

You might also consider Colicchio and Sons. I don't think of it as particularly trendy, but it's more American-style cuisine, and it's near the High Line so it can draw a trendier crowd.

Freeman Alley is a long-time "trendy" place that serves mostly American food. But the young, trendy restaurants these days are opening up in the Lower East Side. If you go down there, you'll find Meatball Shop (extremely popular and trendy, but not fancy), Stanton Social, Schiller's Liquor Bar (which is a restaurant), etc. I sat next to Adrian Brody at the little Greek restaurant across from Stanton Social that serves souvlaki (I can't remember it's name, unfortunately). And I've stood in line behind him at Starbucks down there. So you may find a few demi-celebrities eating, particularly during weekday lunch when things are quieter.

Or you might look at Marble Lane at the Dream Downtown.

You'll find it easier to get into all these places at lunch. If you want to eat dinner there, you have to reserve a couple of weeks in advance at the places that take reservations, and if you want to do any celebrity spotting, don't go before 9. But to be honest, I may not be the best person to make these suggestions. I try my best to avoid trendy restaurants. I'd only eat at Freemans, for instance, at lunch. I'd never have dinner there.

Agree with Doug about Lower East Side, especially Stanton Social. http://thestantonsocial.com/

The other place that is classic NYC which is almost always a winner is Balthazar in Soho. French bistro food though - not American. http://balthazarny.com/

Totally agree with the lively experience known as Balthazar - and you might see some celebs there - and also take home some great pastries/bread.
And I really like their French Onion Soup.

Also - all around Greenwich Villge are some fun places - including many Pizza Pie "legends". The best Margherita pizza I had though was at Motorino's - a few blocks from Greenwich in the East Village. http://motorinopizza.com/

And also take them to one of the great chocolate places - such as Max Brenner - the Bald Man. It's over by Union Square: http://newyork.metromix.com/restaurants/traditional_classic/max-brenner-chocolate-by-greenwich-village/57413/content

Actually - here is the webpage - but there are other great chocolate places in NYC. http://shop.maxbrenner.com/

You should also take the girls up by bustling Times Square - and near there is one of my favorite French Bistros - Tout Va Bien - and I wrote a review about it - under New York. Very authentic - like taking a trip to Frnance - and tres reasonable. http://www.letoutvabien.com/

Another great lunch place: http://www.abckitchennyc.com/

As you can see, there are so many options for NYC. I would narrow it down to 3 choices and then let your daughter pick.

I see Doug has beat me to recommending the Meatball Shop -- but there is now a new branch in the West Village at 64 Greenwich Ave. http://www.themeatballshop.com/ Nothing fancy but very popular and good! Best for lunch as the wait can be long a dinner time.

By the way-

There hasn't been a celebrity at Balthazar since Cats opened.
It is fine for kids but it is an over rated bistro although the breads are spectacular now over run by tourists looking for the ghosts of celebrities.

Max Brenner is OK for kids but not for adults. It is a crowded mediocre place. There are at least ten other spots who make superior chocolate but it is the rare sit down chocolate restaurant.

Finding celebrities is always hit and miss. I have seen them in inexpensive joints and more often just walking abound. Part of the NY culture is to leave them alone.

One day we were at the Meatball Shop and Gaga was eating up the block causing a stir.

If you like seafood, I just went to Flex Mussels, and it was great!. 154 W. 13th St. They also have lobster rolls and all kinds of mussels and clams. The service was VERY good oh and the wine list for you was good too.

Have a fun trip while you are here.

Wow!! Thank you all so much...so helpful! Going to go do my homework now...kind of makes me hungry! Thanks everyone

Hey - the kids would still love a hot choclate at the fountain bar in Max Brenner. And looking at the chocolate display in the front.

You can also catch the subway at nearby Union Square to go up to the Met Museum of Art - if you are planning doing that. Great for kids of all ages.

What would probably make them happy is to take a walk down Broadway from about Eighth Street to Canal Street, there are scores of stores for them and they will love the Chinese Department store and tchotchke farm-Pearl River on B'Way between Grand and Broome.

Take them to the Chinatown Ice Cream Factory afterwards.
http://chinatownicecreamfactory.com/

Chocolate places:

Jacques Torres-multiple locations

Evelyn's-best chocolate value in the city, not the best chocolate. Very nice people.

Economy Candy-has evey imaginable mass produced candy plus some store made stuff. Wonderful place to visit.
____

More Expensive to very expensive

Teuscher-flown in from Switzerland

Kee's-she was a banker now makes bon, bons, macarons and truffles. Exceptional

La Maison du Chocolat

Burdick Chocolate-LA Based

MarieBelle-more arty

ABC Kitchen=great idea. Very pretty place; wide choice on menu including pizza and pasta.

Love it...Pearl River's new categorization=tchotchke farm! Hardly the only one on that stretch!

If you do that Broadway walk that Adu suggests, you can detour a block and take in this place that might wow the kids and the adults, on East 2nd Street just off Bowery.

http://www.johnderian.com/index_home.html

Uno Mas - there are a ton of good/fun places to dine in NYC - that the girls would probably dig - including the Union Square Cafe. It's not only an ongoing favorite of Big Apple diners - and it also provides "big city" atmosphere if that's what they want to experience.

BTW - it's just "up the street" from where you could get a very good hot chocolate at Max Brenner's.

http://www.unionsquarecafe.com/press.html

http://www.unionsquarecafe.com/directions.html

http://www.unionsquarecafe.com/directions.html

Union Square Cafe is a safe bet but I would not place it anywhere near the "trendy" category.

My teenaged nephews think it's way cool to go to the "hidden" places when they visit us in Manhattan.

La Esquina is a great choice. We sat next to George Clooney and his girlfriend that last time we took our nephews.

http://www.esquinanyc.com/

Kuma Inn is another fun one. http://www.kumainn.com/

Also it's not hidden but it is over-the-top and a very "scene-y" spot, Buddakan. http://www.buddakannyc.com/ Because it's a Starr Restaurant, it still attracts its share of celebrities. The nephews loved sitting at the communal table, which you can request when you call for a reservation.

Enjoy!

Fo rmore info about the restaurants listed - including actual menu and prices (the ones you have been given range from modest to big $) look them up on menupages.com

My eperience is that you often see "someone" at Buddakan - but it many not be someone a 14 year old would recognize - and yuo can;t have dinner before 9 pm.

How about Garage in the West Village for lunch? 14 years old is still young enough to be guileless; they might love to have lunch here:

http://garagerest.com/

I like the Meatball shop but not sure a 14 year old would think it's trendy. My daughter liked sitting outside (heck, and inside) at Cafeteria in Chelsea. (Many Yelp reviews seem to use the word "trendy") We've seen a couple celebs there. Great to sit outside and people watch.

freemans in LES off Rivington is oh so cool too. Liked the food and vibe.

Sites

http://freemansrestaurant.com/

Www.cafeteriagroup.com

Buddakan is Asian, so I think it's out of the running, but I agree that it's very cool.