One of New York's most famous restaurants is in the area you are considering. The Four Seasons Restaurant (not to be confused with the Four Seasons Hotel or hotel chain) is a a beautiful Manhattan restaurant and is a premier New York experience. Best of all, the pre-theatre dinner is $55 for a complete dinner, including appetizer, main course, coffee, dessert. Six main courses are offered at this price, including filet mignon. I'll try posting here a link to the the menus, which includes pre-theatre menu.
http://www.fourseasonsrestaurant.com/