To rough it out, very generally, once you get to the west side of the city, route 30 from about Imperial, PA is not a bad road, you can take it all the way to East Liverpool, OH.
As far as getting from town to Imperial, your best bet might be to nicely ask if some native could escort you that far. It's not impossible, but you could avoid a ton of frustration. And make some friends.
Going out of East L, OH, you'll need to pick your way on some back roads to avoid what becomes the 30/7/11 divided highway, like rt 267.
At some point 30 drops off the divided highway and becomes 30/45, take that all the way to Lisbon. Then continue on 45 to Salem.
From Salem, just go on 14 and you're arrowing straight for Cleve. 14 gets really jacked up around Streetsboro, but there are plenty of little side roads to pick your way around that cluster.
After that you're into the exurbs and things get really unpleasant, but I think your best bet would be to get to the Cuyahoga Valley trail as directly a possible, like 303 to Peninsula. I think you can ride that rail trail all the way to downtown, that would need to be verified. But I can't think of any other way I would even suggest riding from the 'urbs into town.
I'm thinking you will be right around your 140 mi. est.
Also, when you're up there, check out the Tremont neighborhood just south of downtown, a cool hood. I don't know if killer little non-chain restaurants are your thing, but if you want some good eatin while you're there, that's where they are.