It all depends on the mood you want.
For the ultimate in fine dining and privacy, Victoria & Alberts is wonderful. You get a special personalized menu with your names and the date. If they know ahead that it is your anniversary, they will write Happy Anniversary on the menu. Ladies get a long stem red rose when they leave. Very special, very romantic.
A window seat at California Grille is always spectacular if you are there for the fireworks. The guy in the table behind us proposed just prior to the fireworks beginning and the waiter videotaped the whole thing for him.
In addition to dining on your balcony, you could have a gourmet "picnic" packed for you along with some nice wine and eat on one of the WDW "beaches". (This is great if the weather is nice and you time it to enjoy the water pageant and Wishes fireworks.)
I am also partial for sentimental reasons to the Portobello Yacht Club in Downtown Disney. We went there on our honeymoon and go back whenever we can. The outdoor tables are lovely, the food is very good. Plus, you can go to Pleasure Island afterwards.
I have found that the best way to insure a great time, no matter where you choose, is the plan ahead and not be afraid to ask-very nicely of course-the restaurant to help you make the evening special. Whether you drop off a special centerpiece or decorations for the table (even if it is just a few yards of tulle for them to tie to the chair backs or something to make it more romantic), or give them your cake top to use on an anniversary cake at the meal's end- let them know its a special occasion. Then follow up the day of by calling the restaurant to touch base. Make yourself more than a name on a reservation sheet. You are sure to have a special night no matter where you choose. Happy Anniversary!
