The students who opt for off-campus housing occupy most of the rental apartments in town. As a result, the best time to look for an apartment is usually in April and May. June and July can still be good, but you will find very few vacancies in August or September. Things pick up again a little bit in November and December as some leave at the end of the fall semester.
When you're renting in Clemson, most landlords will expect that you're a student. Typical questions include what your field of study is, whether or not you're working, and whether you're studying full or part time. If you're not a student, a simple letter of employment will steer landlords away from these lines of inquiry.
Clemson has a top notch bus system that is operated jointly by the town and the school. As a result, it is free for everyone to ride. It is also well organized and typically on time, as it doesn't have to deal with all the issues that plague bus routes in larger cities.
Most of the entertainment in town is also centered on the University. Clemson has a Division I athletics programs, and taking in a Tigers Baseball, Basketball or Football game are all good ways to spend an evening. If you like outdoors activities, getting out on a boat on Lake Hartnell is an option. The nightlife is all centered near the University, so a simple pass up College Avenue should reveal lots of options for grabbing a drink.