Without debate, Highland's should be at the top of your list.
I agree with sheilal's recs, except Hot & Hot (but I am in a small minority on that). Ross Bridge is definitely the best place to stay, although the food is not remarkable. There are too many excellent places in Bham to burn a meal there.
In addition to sheilal's recs, I add George Reis' Ocean and 26 (side by side restaurants; Ocean requires reservations; 26 is walk in). Also, a personal favorite that will definitely require reservartions is Gianmarco - fantastic inventive Italian. There are many standards on the menu that I'm dying to try, but never do because the specials always grab me.
It's in Homewood - down Broadway.
Not formal at all, but reservations strongly recommended almost every night.
Two brothers alternate nights cooking; brought their dad Giovani our of retirement to run the front of the house (he had a place in NY).
I'm not exaggerating when I say everything is excellent. The Snapper in a caper sauce is a signature dish. I can never pass up the specials. The scallops are perfectly done when on the menu; presentation varies.
Also fun, there is a three seat (actually 3 stool) chef's counter; watch all the dishes go by and pick. We've also let the chef pick for us and share several dishes.
Highland's is still a wonderful dining distination here in Bham. Frank Stitt is an amazing chef. His french bistro Chez Fon Fon is authentic and also delicious. A couple of other "tops" is Cafe Dupont downtown and Hot and Hot Fish Club. Outstanding! I've not heard any buzz about Ross Bridge. They had a write up in Birmingham magazine and it sounded really good. But I haven't run across anyone who's dined there yet. I'd love to hear your critique if you go.