I live in the NE US (2000 miles away), but I have to attend a trade show in Las Vegas each year. I often take some time off after the show to photograph in the SW, so I have visited many of the sites in the area.
A few thoughts:
I shoot mostly B&W, but you will kick yourself if you don't pack some colour film and a polarizer.
Zion, Arches, Bryce are all fantastic in their own, different ways, don't try to rush through all of them - especially Zion, and spend several days to be able to get more of a sense for the place. Much of Zion (and in my opinion the most interesting bits) is in deep, narrow canyons or valleys, which means that the shooting day is relatively short - nice for when you are on vacation.
Don't know when you are planning on visiting. During my late April timeframe, the north rim of the Grand Canyon is not accessible, but I have visited the South Rim a few times. Last time was with my teenage daughter who is also a photographer. We had a deal that we would take a peek outside at sunrise, and if the sky looked good, we would go out and shoot, then have breakfast later, if lousy sky, we would sleep in. We were blessed with very few days where we could sleep in
Another SW destination which is nice, although not in Utah is the Valley of Fire in Nevada - great red rock formations and some ancient petroglyphs. About an hour outside of Las Vegas.
Also, not in Utah, but SW are some of the ghost towns of the south, mostly in Nevada or California. Some of my favourites are Bodie, Rhyolite and Berlin. Frisco in Utah is another nice one.
I have not been there, but it is on my list to visit are the Anasazi cliff dwellings in Mesa Verde National Park, Colorado.