it would actually be "built-in" and I suppose you could use it to describe a restaurant. I hear the term "built-in" most often in relation to houses and cars.
"Our house has a built-in fireplace." "My car has a built-in phone charger." "My home has a built-in restaurant."
Generally it is used to describe things that you would not necessarily expect to be included, but I don't see a huge problem with saying the hotel has a built-in restaurant.
As for your "reservation for a room at a hotel", it doesn't sound awkward at all to me. I am sure I have actually said this before on multiple occasions. It's not redundant by specifying that you are reserving a room in a hotel because there are other establishments that you could reserve a room in (bed and breakfast, motel, etc.).
Hope this helps :)