Everyone has given you great ideas, but I'd like to add that if this is your first trip to London I would urge you to see a show at the National Theatre, a true treasure. There are usually several shows happening at the same time and you can eat right there in the complex (I prefer the self-service cafeteria style place, but the pricier option is fine, too). (Also depending on the show, I love the intimacy of the Donmar Warehouse.) I enjoy the West End, too, but it's not as condensed as Broadway so it's hard to give you a food idea without knowing for sure where you'll end up. But close to many of the theatres is Covent Garden and there are many good places for a meal there. Enjoy your first trip to England. I was last in London about three years ago and I love all of the free museums and the theatre and I also very highly recommend taking a walking tour (or two) from London Walks where you can take an Oscar Wilde walk or if you are a Christie fan, you might also enjoy the Sherlock Holmes walk. I've done at least ten of them over several visits and have enjoyed them all as you see parts of the city you would never see on your own. Enjoy! It's a great city.