Biking is definitely the best way to go. There are even bike lanes out to the nearby Kroger so I could go grocery shopping without a car. Of course the campus is quite hilly, but I think of it as getting a solid workout everyday. Fast, easy, and very fun.
Parking services is notorious for byzantine regulations and parking is often in short supply in the most popular areas.
The UGA buses are quite convenient, especially for first-years living on campus. They also run to a few nearby apartment complexes at night. You can cover almost all of campus in a bus in less than 20 minutes or maybe 25 during the busiest times. Just make sure to learn the bus routes as soon as you get on campus. As a UGA student, you also get free fare on the city buses which go out to WalMart, Target, etc., so if you're up for learning those bus schedules you can use them as well.