Utah is a big place with several areas that attract photographers. I have spent my time in Zion, Bryce, the Moab and Blanding areas, and Monument Valley. (The entrance to MV is in Utah; much of the Navajo nation 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: (See my blog post on photographing the House on Fire ruins)
Natural Bridges NM: Natural Bridges NM website