First rule about Atlanta is that a car is the best way to get around. The mass transit system here is worthless. The entire metro Atlanta area was built around cars and highways. If you are going to be here for more than a day or two, I highly recommend getting a rental car. Either that or you are going to spend a lot of money on cabs because everything is really spread out here.

The Galleria is about 10 miles northwest of Atlanta. That sounds close, but depending on the time of day that could much longer to get downtown that you would expect. There are quite a few restaurants around the Cumberland Mall area, which as QuickX5 said, is located just across the street from the Galleria. If you are looking for additional restaurants and pubs I would suggest going to Vinings. It is a nice, fairly upscale area with a few good restaurants and bars and is only a mile or two from the Galleria. Vinings would be an easy/cheap cab ride.

If you are looking for more excitement then you would probably want to go to Midtown or Buckhead, which are a little further from where you are staying and closer to Atlanta.