In Ohio if you want to save some money on the tolls you could take Rt-2 over towards Cleveland and catch I-480 around the city to the south. (very similar to busskipper's route but skipping a good section of the tpk) I-480 will eventually drop you down to the turnpike with about 50 or 60 miles left in the state.
**If you really want to avoid the tolls take Rt-2/I-90 all the way through Cleveland and out to the east side and catch Rt-11 south to the TPK (only a few exist from the PA line) or just go over into PA on I-90 and catch I-79 near Erie and go south from there but the toll savings may be eaten up in fuel costs.
I too feel that once you're around Pittsburgh you should drop south towards I-68 and stay off the PA TPK as much as possible.