The list is endless...almost. Where you coming from? The norther end has great stuff in Cache County, Bear Lake, and then up into Idaho. The uintahs, around Zions or above Cedar City, or....you get the point.
I lived in Utah for 8 years for school, it's a really beautiful place.
It depends on what time of year, you can be pretty comfortable down in the Southern part of the state deep into the fall, and early spring. On the other hand, go North and stay up in elevation if you are taking time off in the summer.
Arches, Moab and Bryce in the cool weather. Bear Lake, Ogden, day trips in the canyons (Emmigration, Little and Big Cottonwood) in the summer.