There's plenty to do in Birmingham. Stay downtown at the Redmont Hotel on 5th Ave N. (cool heated rooftop bar), head over to the Avondale area (several good restaurants and a couple of cool bars + Avondale Brewery. Lakeview District a good restaurant called 5 and Slice pizza, Have a drink at The Garage (voted as one of the best bars in the US by Playboy a while back). You also have the Loft District on 1st and 2nd Ave N. a few good bars here as well as El Barrio (hip Mexican restaurant that's very good)
Things to do during the day, head over the mountain to Homewood and go by Steel City Pops for ice cream then drive around some of the cool neighborhoods. Head over to Mountain Brook and drive around English Village, Crestline Village (Smith's Variety) and Mountain Brook Village - nice areas to see as well with good restaurants. Also take a winding drive down Highland Ave. You can get a nice view of downtown Birmingham at sunset from the top of Vulcan. There's the Birmingham Museum of Art as well as Barber Motorsports Museum. Hop on a Zyp Bike (locations all over Birmingham) and ride over to Rail Road Park and then grab a beer at Good People Brewing Co.
White tablecloth dining Hot & Hot Fish Club, Bottaga, Highlands Bar & Grill, Gianmarco's
For live music Alabama Theater, Lyric Theater, WorkPlay, IronCity, Saturn and Tin Roof
Golf - Highland Park (short course but well kept and fun)
http://www.movoto.com/guide/birmingham-al/16-best-bars-in-birmingham-2016/