Speaking as someone who just finished a two week road trip from Chicago to Virginia and back...don't worry about finding hotels/motels.
Seriously, just drive as long as you feel like, and when you're ready to stop, start looking at the "lodging" signs on the interstate exits. You'll find the chain you're looking for inside an hour at most. And the only time I found a place full up, it was because there was a huge bigwig gathering in town.
Yeah. Actually, it turned out even better than that---at a rest area about two hours before I planned to stop for the night, I picked up a book of ads for motels throughout the Commonwealth of Pennsylvania---and was able to pick out a few in the right distance range, and get the cheap one. "Budget Inn" of Clearfield, PA. Perfectly adequate. Even had power!