Utah is a big place with several areas that attract photographers. I have spent my time in the Moab and Blanding areas and Monument Valley. (The entrance to MV is in Utah; much of the Navajo Park is in Arizona.)
As usual, your first step should be to purchase Martres’ Photographing the Southwest Vol.1: Southern Utah, 3rd Edition (March 2015), available at Amazon.
Another excellent source of information is at Americansouthwest.net. There are sections for each state in the area, often with maps.
Moab: Discover Moab website
Canyonlands Information: Canyonlands Natural History Association, Canyonlands NPS website
Arches NP: Arches NPS website
Hovenweep NM: Hovenweep NPS website
House on Fire/Mule Canyon:
Natural Bridges NM: Natural Bridges NM website