Couple of ideas, though they are a ways from Bryce Canyon:

SE Utah has the Mecca for off-roading, in the Moab area. You could wheel there for a couple weeks without getting bored. And Arches NP is just down the road.

Elephant Hill trail at Canyonlands NP is a moderate trail that is very cool and scenic, do the short hikes to the Joint Trail and the Colorado/Green rivers confluence. No dogs, though.

Steve Carlson - 95 Trooper LS expo rig
Serenity now!