Natural History Museum on a rainy day? Too noisy? Too educational? I love the big bones. If they are science minded, the Rose Earth and Science Museum is next door with quite a number of very cool, high-tech features.

What do the kids like to eat? Plenty of places that aren't a rip-off. If they are adventurous, I'd suggest Inakaya on W.40th as a real theatrical experience. Sit at the sushi grill bar, where the waiters shout in unison when food is ready to go to the table:

http://www.inakayany.com/

or Lan Sheng for Szechuan on west 39th, or Osteria al Doge on 44th for individual thin crust pizzas in an elegant setting (go hungry). I also think B.L.T. for Belgian mussels and frites is a bargain (but noisy!)

But there are safer bets with hamburgers and french fries. My pick would be either Angus McIndoe or Joe Allen's. Better reserve wherever you want soon.

For breakfasts, try Le Pain Quotidien on 40th just off 6th.

I'm sorry -- I meant BXL Belgian Cafe

http://bxlcafe.pregraphic.com/

It is very friendly and middle class, but it very much attracts people who like Belgian beer. I have seen more than one pre-teen/early teen there with their folks, but it has an old fashioned NYC Times Square beer-bar feel, so if you want something light and bright, that's not it.

Have you considered Ellen's Stardust Diner? Basic diner fare but the wait staff are resting b'way chorus boys and girls and they do some very nice performances. You can see the menu and prices on menupages.com.

At that age my girls would have preferred something more exotic - but they liked tying all sorts of different cuisines - and preferred trendy.

You might want to visit the high line and find food in the Chelsea Market.

They are decent eaters. American, Italian, Chinese, and some French fare. We have done Ellen's Stardust Diner (so much fun!), but thanks for the suggestion. Trendy is definitely an option, but within reason. I prefer not to spend over $100 total for dinner. We have eaten at Thalia's, which we did not like very much. However, maybe an ambience similar to it would be suitable. Thank you so much for the suggestions so far!

Katherine, I have booked the Garden Inn on 35th for Xmas week. Let me know how it is.

I like that Hilton - larger rooms for NYC - good location for theater - enjoy!

Maybe Pigalle? I don't think the food is off the charts, but it is easy and fun and fairly decent.

http://www.pigallenyc.com/

There is another place I think it is a lot of fun with is the restaurant at the Crowne Plaza hotel. It sits on the 3rd floor right above Times Square at 47th, with picture windows looking down into all the wild hubub below. I had a surprisingly good ($16) hamburger there, but that is all I can report. I would not go looking for great food, and would only go if I was guaranteed a window table upon reserving:

http://www.cpmanhattantimessquare.com/brasserie-1605.html

http://www.menupages.com/restaurants/brasserie-1605/menu

Assuming the kids are going to eat desserts and drink more than water, you are pushing your $100 ceiling at most of these places.

My two favorite places to take young teens in theater district are Becco and Kellari Tavern. Both are affordable but upscale enough to seem special. Both have food kids like. The waiters offering more servings of pasta from hugh frying pans are fun. Kellari with the raw fish display and Greek specialities is not most kids usual dinner. Plus I love the dessert cookies.

I was just going to recommend Becco. For Pizza, John's, though the line can be long pre-theatre especially in nice weather. I also like Five Napkin Burger and Gallo Nero. Gallo Nero is smallish but really cute with good service and decent prices. It's one of my favorites in the area -- maybe only 10 tables but the girls might find it sophisticated, which would be fun. Five Napkin Burger's interior is more upscale than a restaurant with "burger" in the name would imply.

Thank you! So many great suggestions! I will make sure to look into all of them. I would prefer to keep it around $100-$115 range...
@bethke14 We actually have been to John's quite a few times, it's always very good, and reasonable.