Downtown Kent and the Kent State campus are very walkable — the two areas are essentially connected, and everything worth seeing is within a comfortable walk of each other. Most students and visitors get around on foot or bicycle, and the Portage Hike and Bike Trail makes cycling a practical option for moving around town.
Areawide Coordinated Transportation (ACTA) runs local bus service in the Kent area, connecting the university and downtown to surrounding neighborhoods. It's functional but limited in frequency.
If you're planning a day trip to Cuyahoga Valley National Park or anywhere else in the region, you'll need a car. The trail system in the national park is excellent, but getting there from Kent without a vehicle is not practical.