AZ is OK as anyone can carry concealed.
That's not entirely correct. You have to be legally able (under both state and federal law) to own a firearm in order to carry one, open or concealed. A permit is required to carry into a restaurant or bar that serves alcohol. "No gun" signs have the force of law, statewide. Always get trained and learn the law before you carry a gun.
Utah has strict gun laws, especially near urban areas.
It is, however, straightforward to get a Utah Concealed Firearms Permit without being a resident of Utah.
New Mexico allows open carry but only honors permits from some other states.
TX has complex laws.
Both states are gun-friendly and honor many other states' permits.