Georgia Southern University is a large school, and the students represent a large percentage of the total population of the town. This means that your apartment hunt needs to take the schedule of the students into account. Ideally, you should try to look for an apartment during June and July. Avoid looking in September if at all possible, as supply will be at an all time low.
Statesboro landlords take professionalism and manners very seriously. Show up on time for your appointments, dress well, and be polite and professional when speaking with landlords. If you appear irresponsible or rude, they will draw conclusions quickly about what kind of tenant you might be, and you will find it difficult to find an apartment.
There is a good public transportation system in place that shuttles people to and from Georgia Southern University. However, this system is typically only active when the University at large is. To be able to be mobile throughout the year, having a car in Statesboro is a very good idea.
The Center for Wildlife Education at the University is a great place to visit if you enjoy learning about nature, or if you have a family. Splash in the Boro is a great water park found in Statesboro. Statesboro has some great dining options, including the South and Vine Public House, or Coconut if you feel like trying some local Thai food.