Both Kansas in Lawrence and Kansas State in Manhattan are close to some trails. I can't speak as to how much (if any) the college teams run on the trails, but I've lived in both cities and would make the short drive out to the parks whenever I could. Your best bet might be KU.
Kansas State / Manhattan
Konza Prairie (hilly trail on the Kansas prairie) about 10 minutes south of town
Fancy Creek and Randolph State Parks (semi hilly trails in woods) about 15 minutes north of town
Linear Trail (crushed gravel trail through the city)
Kansas / Lawrence
Riverfront Trail (just north of downtown, 9 mile crushed gravel levee trail, also 8 mile flat wooded mountain bike trail)
Clinton Lake State Park (semi hilly trails in the woods) about 10 minutes west of town
If you are willing to drive further out (30 minutes or so), there's Perry State Park and Kill Creek Park with some more trails.