How long do you want to be riding?
I'm thinking the series of national parks of Southern Utah (going park to park). Zion, Bryce, Capital Reef- or to the east side of the state with Canyonlands and Arches.
We rode in Zion, and it was great!! Even tho the roads were narrow, cars gave us wide berth (although we did have to hitch a ride through the tunnel part as they were doing construction). There were the RV's that sometimes came too close, but you're going to truthfully have that in any national park where the scenery makes you want to gawk as you drive, IMO.
I just LOVE the Southwest. Can't get enough.
http://www.utah.com/nationalparks/
I've heard Glacier NP is amazing, too, but have not ever been there so I don't know what the road conditions are like, nor do I know about lodging and distance between.