To be totally honest. Ohio doesn't offer much for trout fishing. If you mean trout streams, the nearest to Kent is probably over an hour drive. Mohican State Park area. However, there are a few lakes in NE Ohio that get stocked with trout. Punderson State Park comes to mind, and I think it is less than 30 miles from KSU. It probably takes 40-45 minutes to get there from KSU. There is a campground there, and cabin rentals and it's a nice little park. There might be one or two lakes even closer that are stocked with trout, but I didn't look it up. You could check the ODNR website.
If you are into private trout clubs, I know of one (
Pine Lake) that is only about 20 miles, though it probably takes a good 40 minutes to get there from KSU. They have a couple of ponds and a small creek that they stock. I used to live in the area and checked it out. It was nice then, and even looks nicer now based on the website. Reminded me of PA. Very peaceful. I didn't join though. They used to have a small fly shop (Orvis I think) over 20 years ago, and it was up for sale. I was considering buying it, but after crunching the numbers, I would have had to keep my regular job. So I decided not to pursue it. I don't know if the fly shop is still there, but it probably is.