They are too far apart. I would stay at or near each park. Zion has the least best options, Bryce is better and Canyonlands better still. Don't forget to visit Capital Reef NP, you'll pass through it going between Canyonlands and Bryce. Just as beautiful and underrated IMHO. There are lots to choose from, I have stayed at several, they were all ok, nothing stood out. To help here are some options:
Moab Campgrounds
Bryce Campgrounds
Zion Campgrounds