Above and beyond: The Highlands Bar and Grill. If you eat nowhere else, eat here. This restaurant is responsible for everything every southern chef is doing.
Frank Stitt is a gentleman and one of the best and most creative cooks in the world.
The food, service, atmosphere, beverages, and everything else you can imagine at the Highlands is absolutely first rate.
Mr. Stitt's other places are also great: Bottega and Chez Fonfon. Another higher end place is the Hot and Hot Fish Club, an established restaurant and chef that are arguably hitting their peak.
Outside of that, Jim n Nicks BBQ is a pretty big draw. They are originators of this group, the Fatback Collective, of southern cooks that promotes humane, well raised, heritage pork. The FBC has a multi year breeding program and a processing facility now that provides pigs and pork to its members, including Jim 'n Nick's. Nick is also a hell of nice guy, and knows how to cook a hogs and have a good time.
Almost any Mexican or Middle Eastern food you run into in Birmingham tends to be good, as there are a ton of Latin Americans working in agriculture outside the city, and a ton of Lebanese have settled all over Alabama during various bad times.
But seriously, the Highlands. Even if you eat alone at the bar. Maybe especially alone at the bar. Then you can't embarrass yourself.