A kitchen is a room used to cook and prepare food. They are located in restaurants, houses, and apartments. Facilities such as hospitals and schools have large kitchens.
The Xavier Mansion has a rather large kitchen. Gambit and Jean Grey cook in there, often having to put up with each other. It got particularly bad on Christmas Eve when Gambit kept wanting to spice up Jean's food.
The Morlocks also had a kitchen for the entire group, though it was run down and not as nice as the X-Men's.