Capitol Limited from Chicago to Cleveland (and on to DC) has walk-on bicycle service, which means, unlike the Empire Builder, which, I think, limits their bicycle handling to baggage stops, you can get on/off at any spot with your bike as long as you have a reserved spot for the bike. There is a partially complete trail from just outside of Toledo to just outside of Cleveland.
North Coast Inland Trail
It's about 120 miles from Toledo to Cleveland, but I think only half of that would be on the trail, and I've never ridden the trail, so I don't know what kind of riding it is. Sandusky is about halfway between (but not directly on the N. Coast Inland Trail) and also has a train station. Also in the north west Ohio area are some Lake Erie islands. I think they are a fun trip on bicycle and scenic, but not a good way to get high miles on a bike, as the islands maybe 5 to 10 miles long, so you spend as long on the ferry over as you do biking. If it were possible, I think it'd be good trip to bike from Toledo to the Miller Boat Line on Cawtawba, take a ferry to Put-In-Bay, and spend the night there, then take a ferry to Kelly's Island and boat to Sandusky. Problem is that, while I thought you could get a boat from Kelly's Island to Sandusky, I don't see it on the map. I only see a ferry back to the peninsula, which, thanks to Cawtawba Bay, and the fact that Route 2 is limited access, motor vehicle-only, the trip to Sandusky is pretty much another, full day trip if you went that way. Might even be easier just to backtrack to Toledo and get back on the train there. I've actually used the Route 2 bridge to get my bike between Cawtawba and Sandusky, but it's illegal and it certainly wasn't pleasant. I just didn't have the luxury of a 60 mile detour around the bay.
Also, depending where in Cleveland you were going, you could overshoot by one stop and get off the train in Alliance (at 3am, unfortunately), and go west until you hit the Ohio and Erie Towpath which will then take you into Cleveland. The towpath will be largely unpaved, though, and if it's wet, it may not be great riding, but if it's dry, I think it'd be pleasant, and the surface is very smooth.