Athens is liveliest when the University of Georgia is in session — fall semester (late August through December) and spring (January through April). Football weekends in autumn are enormously busy: the city fills with 90,000 fans, hotels book out months in advance, and everything around downtown is loud and crowded. If you are coming for the football, plan well ahead. If you are coming for anything else, avoid home-game weekends.
Spring is the most comfortable season for walking around: temperatures in the 60s and 70s Fahrenheit, the campus trees in bloom, and enough students around to keep the bar and restaurant scene active. Summer is hot and humid, and the city quiets down considerably when the students leave.