My husband and I were out in the Moab area last fall and did some road and off-road biking on our tandems. We did a tour of Canyonlands NP on the road tandem and it had great scenery with a few small hills. The motorists were very courteous and numerous people approached us at the rest stops and overlooks in the park to talk biking.
We decided not to do Arches NP by bike as it has a much higher level of traffic and no shoulders.
We biked on some of the other roads around Moab without problems. I would second the previous suggestion regarding the routes on the skinny tire festival website.
Our biggest issue was carrying enough water along with us. Very few sources of water out on the roads.