Depending on how long you have before your trip you might want to consider getting a Utah or Florida permit. Either is recognized in Arizona and would allow you to carry concealed as well as openly. It's always nice to be able to conceal your gun if it's cold or raining and you want to wear a coat. Or you may want to arrange to take a CCW class in Arizona while you're there and qualify for your Arizona permit for next time. Some places also offer a class that will cover both Arizona and Utah.
I've carried openly in Arizona, but I now have Arizona, Utah and Florida permits, and I like the flexibility.