Tucked away in the back corner of New Fantasyland is Be Our Guest restaurant, one of Disney World's many dining establishments. Opened in 2012, it was a part of the Fantasyland expansion. This specific corner of the land is Beauty and the Beast-themed, as it's surrounded by Enchanted Tales With Belle and Gaston's Tavern. Beast's castle uses the crafty forced perspective trick Disney is fond of, as it sits high atop a mountain away from everyone else.
For breakfast and lunch the restaurant is a quick service place, but for dinner it is a full table service restaurant. You will need to get reservations for this place, but frankly they aren't too hard to get for breakfast or lunch. Dinner reservations are a lot harder to land, as guests can meet the Beast at the end of the meal. This is the only area in both American Disney theme parks where you can meet the Beast.
I prefer to go for breakfast, as you can normally get into the park before it opens, resulting in some stunning empty park pictures. The food isn't bad. I've eaten here a handful of times and never had a bad meal. I will say, though, the grey stuff is indeed delicious. Lumiere did not lie. Price-wise, you're looking at $5 (for the grey stuff on a cupcake) to $30, depending on what you get. You can dine in the main ballroom where Belle and Beast danced, in the West Wing (where Belle wasn't supposed to go), or in Belle's library. All three are excellent choices, as they are themed beautifully.