There is SO much to see in Utah. One could spend months/years there and not see it all. In fact, we met a couple who had visited Utah then decided to move there for a couple of years to see all there was to see. That was 25 years ago and they said they still hadn't seen it all.
Bryce is a must see. We stayed at Ruby's and took the Jeep into the park but there are shuttles there as well. Hwy 12 can be intimidating, especially the section called the Hogback, but it's a spectacular drive and one you should not miss. The loop around Fish Lake which is west of Capitol Reef is a wonderful day drive. We stayed in Torrey and made the drive from there in the Jeep. Just beautiful. Goblin State Park is a bit out of the way but worth the stop. Arches & Canyonlands are near Moab but don't miss Dead Horse Point State Park. Seeing the sunset from the point is something you should do too. Hwy 128 is another spectacular drive and has some wonderful BLM campgrounds along it.
Hopefully, we'll be back in that area next year!