I just did Cleveland, OH to Pittsburgh through New Philadelphia, OH and Steubenville, OH. Hope, someone find it useful:

1. Very good trail Independence, OH -> Bolivar, OH. 3 detours: 1 minor, 1 near Akron, 1 around unfinished part of the trail in Massillon, OH.
2. New Philadelphia to Bowerstown, very pleasant ride, rural roads, suggested rest place: park in Sherrodsville, OH with picnic benches and a restroom right before the bridge.
3. Bowerstown -> Jewett by Conotton Creek trail was very pleasant experience. Trail is in perfect shape.
4. Jewett -> Steubenville. I took a route suggested by google maps: https://goo.gl/maps/j0Z61 (with my corrections to avoid Route 22)
this route has a number of problems:
* huge climb about 2 miles out of Jewett. A lot of hazmat trucks back and forth with very narrow shoulder.
* Route 22 although not a limited access highway before Bloomingdale, OH , but looks and feels pretty much like it. Avoiding it means some not very steep climbs.
* Small part of route 22 is unavoidable without making huge detour.
* Very steep climb on Caditz road at the end seems unavoidable as well.
This path is doable but I would look for an alternative
5. Steubenville -> Pittsburgh. With the demolition of Ft. Steuben bridge the only legal bridge out of Steubenville is Market street bridge. I took it, made a right and took the Archer Hill road.
This is a doable climb even with a loaded touring bike, I expected it to be much worse than that. Nice decent onto a panhandle trail, and following google maps from the end of the trail to Pittsburgh. https://goo.gl/maps/Fpoc3
Steep climb in Crafton.

Feel free to ask questions.