As is the case with most college towns, there is a bit of an exodus from Athens apartments at the same time every year. Usually, students start giving their notice in April or May, and start leaving in May or June. If you start looking right at the start of this period, you should have your pick of apartments.
When you speak to Athens landlords, ask them what they require as part of their application process before you even meet with them. That way, you can be sure to be prepared. For instance, if they need to know your employment status, you can get a letter of employment prepared before you meet with them, allowing you to apply on the spot if you like the apartment.
The small population of Athens makes it perfectly navigable by foot. You'll notice a lot of cars on the streets though, as most locals drive almost everywhere they go. The University has a few public transportation services, mostly reserved for special occasions and for navigating the campus itself.
The University is a great place to be entertained, as there are several groups on campus that perform regularly. The School of Theatre, and the Comedy for the Masses sketch comedy troupe are both good bets. If you'd rather get outside for your recreation, head out to Wayne National Forest. Court Street near the University and Union Street are where the most bars are located, with The Union being the most well known.