We have had great birthday experiences at a few signature restaurants. You need to find the one that fits your party the best. Here are my comments on Signature experiences we've had:
Narcoosee's (GF): My favorite signature restaurant. Not too formal, excellent food (the lobster is as good as they say). It's a little noisy which makes for good boisterous celebration, and great venue for fireworks at the Magic Kingdom. Plus you will walk around the GF grounds after dinner which is great too. Perhaps grab a post-dinner cocktail at Mizner's and listen to the band in the lobby.
California Grille (Contemporary): Good food, very good view, but a little bit of a service factory. The demand to eat at this venue is very high and they want to meet as much as they can. This does not lead to a poor experience, but it doesn't give you the birthday celebration time you may desire.
Citricos (GF): I really like this Mediterranean-themed restaurant. The service is very good -- they seem to adjust to the personality of a party very well here. Our crowd tends to have a lot of peronality. The menu is creative and the food is very well prepared.
Chefs de France (Epcot): A hoot! I really enjoy this restaurant, particularly because I have a deep, abinding love for their braised short ribs and papardelle. Again, this is a noisy place, but it is downright beautiful in the late day sun or after dark.
Yachtsman Steakhouse (Yacht Club): Primarily a "prime" steakhouse, the fish/seafood and other offerings pleased my non-steak eating compatriots. Dessert here is something special. Service is a bit formal and the wine list is pricey. The restaurant is quieter and the tables spaced for more intimate dining and conversation with your party. I like to sit near the windows that overlook the pool, others dislike being near the pool. I've eaten here once and I will return.
bluezoo (Dolphin): Best fish dishes on property. Hip decor, very good service. I consider this more of a date spot than a party of three, but that's probably because the time I ate there it was only with my wife.
Shula's (Dolphin): These upscale steakhouses are great. I haven't eaten at the one here because I can eat at them other places, like near my home. If that isn't in the cards for you, consider giving it a try if steak and lobster are things you'd like to eat.
Il Mulino (Swan): I have eaten at the one in New York -- It's great. This one gets good reviews as well. I really like the decor.
Brown Derby (DHS): Great old-school meal. It's large layout and spread-out seating afford a relatively intimate setting even though it kind of looks like a warehouse when you first go in. The setting and experience don't scream "special event dining" to me, but I really like the restaurant.
Non Signature:
le Cellier: I don't think this restaurant deserves its mythic status, but I am a big fan. It's a very enjoyable meal with friendly, informal service.
Yak and Yeti: I inexplicably love this restaurant. The food is solid, but not phenomenal, and not unlike food I can get at a PF Chang's or a local asian restaurant. But I like the decor, the setting in AK is great, they have a really nice bar, and the service is spot-on. They were also patient and attentive with us as we hung out at the table and talked after our meal for a bit.
Casey's (MK): You want to make me happy on my birthday? Get me a hot dog and fries and a nice seat with a view of Main Street and Cinderella's Castle. After all -- it is the joys of experience and not the joys of excess that build lasting memories.