Really? Traverse City too cold for you? LOL That is relatively balmy compared to Houghton, MI--have a relative who lives up there. You'd be missing a lot if you didn't go take a gander at Copper Harbor, Grand Marias, Taquamanon Falls, or even the soo.
As far as Ohio: If you're into roller coasters there is Cedar Point.
Vermillion, OH is a nice little town--or was; its been a while since I was there.
In fact, if you're not in a hurry just get off the freeway at route 4, take it north to route 6 and take 6 East across instead of the Turnpike. You'll save some tolls and have better views. Around Cleveland hop on 2/20 to continue.