With enough vacant apartments to meet the demand, there doesn't seem to be a bad season to look for rental apartments in Augusta. One time to avoid looking though, is around the Master's tournament. Many owners of private rental accommodations will rent them out short-term during the tournament to tourists, often for inflated prices.
Augusta landlords are going to need to see how you can pay for your apartment. Credit history, a letter confirming employment or a letter confirming your scholarship are all good ways to prove your financial stability to landlords. If you have prior landlords who will vouch for your ability to meet rent responsibilities, even better.
Augusta Public Transit operates buses within the city that provide pretty good ways to move between the more popular streets and neighborhoods. However, the entire city isn't covered, and there are outlying potions of Augusta that would be very frustrating to try and reach without a car. Although it can get extremely hot in the summer, a bicycle also makes a practical vehicle for much of the year.
Augusta is full of historic sites worth touring, including the Boyhood Home of Woodrow Wilson. The greatest golf event in the world is held here in April, and although tickets are difficult to get, passes to watch the best golfers in the world play their practice rounds are certainly possible to come by. If you prefer a dive bar to the most elite sporting event in the world, head to Joe's Underground café for cheap beer and live music.