Cathy-
Your problem will be choosing from among the wonderful restaurants. We've spent 5 days during Christmas at the Rihga Royal Hotel, across the street from the Hilton. Here are some tips.
For a great (albeit expensive) meal, go to The Modern - half a block from the Hilton. It is next to the Museum of Modern Art and is brand new. The owner is Danny Meyers, owner of the top-rated Gramercy Tavern and Union Square. You can arrange for a very fancy meal in the Dining Room, or a more casual meal in the Bar (that's where we went). It was wonderful. The Dining Room overlooks a MOMA garden. If you're interested, be sure to call way in advance for reservations.
Our suite at the hotel did not include a kitchen, so we usually had brunch and a dinner before the theater. I believe you have free continental breakfast at the Hilton. The Europa Cafe is one block from the Manhattan Club on 57th and 7th. It's like a little french bistro and we love it - we've gone every year for five years. Brunch or lunch would be great there. There is also a new french place on 7th between 58th and 59th (I think). The translated name is "The Daily Bread" but the actual name is in French. Good for continental breakfasts and a good place to stop before you go home to get some wonderful breads and pastries to take with you.
In terms of ethnic, there is a well known Greek restaurant called Molyvos that's also one block from the Manhattan Club. The food is super but I have to say the service was not great on our last two visits. Remi, a moderate upscale Italian, is near the Hilton on 53rd between 6th and 7th. We've always had great meals there. On the cheaper side, Maristella is near the Holton and is good Italian food.
Don't be afraid to travel further down to the theater district - lots of great choices. One of our favorites is an Italian on Restaurant Row, Orso - 46th between 8th and 9th. Again, advance reservations needed. Don't forget to start with an order of pizza bread and don't be surprised if you see some Broadway stars there. Lattanzis is another great Italian on this street - we've been there (and to Orso) very often. Some people speak highly of Carmines - VERY Italian but a bit of a madhouse. And if you like Turkish food, Darvish is also in the theater district and is both good and reasonable. First time there we had a prix-fixe pre-theater menu - 3 courses for $20!
That should be a good start. You will be in an extraordinary location. Our only problem with the Hilton Club was the wait for the elevators, but I'm not really the patient type! Have a great time!
. Want to make reservations at great seafood or ethnic (or anything but Italan) restaurants that we can walk to from those two places.