Flying Fish is my favorite WDW restaurant. DH and I spent our 3rd anniversary there, and will be returning for our 5th anniversary, as well. We have been there a few other times on non-special occasions.
I really like their signature seafood dish - potato wrapped red snapper. The potato is crisp on the outside and the fish is soft and tender on the inside. They used to serve it with a leek fondue (I'm not sure if it is still served with the snapper), but it was incredible! This dish really turned me onto leeks in a big way.
My husband loves his tuna - for him, the rarer, the better. And he loves the tuna at Flying Fish - the quality is excellent. DH is a fisherman, and I grew up at a marina, so we are used to fresh, top quality seafood.
Don't forget to save room for dessert. I could live off of the Banana Napoleon!
BTW, I noticed you are nearby, in Rumson. DH grew up in Spring Lake, and I grew up in Brielle. We currently live in Point Pleasant. It's a small world!