I'll be driving the turnpike from Breezewood west, headed to Cleveland. Are there any places of interest within a few miles of an exit where I can walk around a bit to break up the drive?

I would jump off at the Monroeville exit and hit Moio's Italian Bakery...yummy Cannoli!

Depends how define a few miles. Fallingwater, the Frank Lloyd Wright house, is about 20 miles off the turnpike at the Donegal exit. A very worthwhile stop.

Don't speed, especially around curves or you might get a "break up" of the drive you don't especially want.

If you enjoy architecture, detour onto 376 towards Pittsburgh and take the Oakland exit. Head to the Cathedral of Learning on the campus of the University of Pittsburgh (a short drive from the exit). You will feel as if you walked into a huge castle. Stop by the Visitor's Center to take a guided or self-guided tour of the Nationality Rooms. (Cost--about $2 each.) There are about 25 or so classrooms which are designed in the style of various countries--e.g. the English room is like the House of Commons and the Irish room is like an old abbey. I like the German room with the stained glass windows of Grimm's fairy tales. It's all fascinating!
Also, check out the website for the Pennsylvania Turnpike before you go to see about lane closures for construction.