To find an apartment you're going to want to be the first on the ground in order to get a great place. May is a fantastic time to look, as this is when the recent crop of graduates is likely moving our of their prime University apartments.
There are enough reasonably priced rental units in Kent that you shouldn't have to start too early to find a great place. As long as you give yourself one to two months to complete your search you should be able to find an apartment right in Kent.
Make sure to let the landlords know that you're looking for an apartment in Kent itself, and that you're not scouring the entire Akron area. Lots of people come out to Kent just to get a cheaper place to stay, but if you let the landlord know that you actually want to be in Kent for the location, it can help make your case for the place.
Kent is both a cycling and pedestrian friendly city. Combine that with better than average bus routes and a cheap taxi service, and it quickly becomes clear that you can get along just fine without a car. If you absolutely need a car, the University has a Zipcar car share program that provides auto access to those without one with them while at school.
Canoeing is popular with the locals, as the Cuyahoga river provides a perfect venue. You can rent canoes, go on group excursions, and take lessons if you're a beginner. For evening fun, head down to Main Street or Water Street to take in a local eatery or bar.