Aside from UGA, Athens is home to one of the most famous music scenes in the country. The best places to go hear some great live music would be at the Georgia Theater, or the 40 Watt. The Georgia Theater is where your more mainstream acts, such as Robert Earl Keen or the Dave Matthews Cover Band would play.
The 40 Watt hosts more Indie type music and always has a diverse list of great acts coming through. The biggest venue though is the Classic Center, which would host the biggest of acts that would ever come to Athens. The Classic Center is downtown, as are the other two places mentioned above.