I actually recently celebrated my 21st birthday at Crystal Palace for dinner with Pooh and friends. That's a great place for someone of any age to celebrate! It's a buffet, so there's bound to be something for everyone on the menu, they bring you a birthday cupcake and card from Pooh and friends, AND there's really good character interaction. At one point during the dinner, they get all the kids up there to march around the restaurant with Pooh, Eeyore, Tigger, and Piglet as they sing and dance. It's really cute.
You may also want to look into Chef Mickey's or Liberty Tree Tavern. But I like Crystal Palace the most.