I lived in Flagstaff for five years, and when I was a paramedic, spent a lot of time in Tuba City and other parts of the reservation flying patients out of there.
It's an entirely different world and culture. The Navajo, in my opinion, are very docile, and despite it being a run down and very poor place, I've never felt unsafe spending time on the reservation. That said, the Navajo have a high incidence of inter-family violent crime and rape, and of course alcoholism. It seemed the prefix of much of the illness on the reservation was alcohol, lots of GI bleeds, alcohol/assualts (blunt trauma), etc. Tons of renal patients from all the diabetes/obesity.
As far as the work environment, a lot of people have good experiences. I never had a negative experience flying patients out of hospitals all over the Navajo reservation. Always friendly staff, etc. But I did find communicating with my patients difficult, because culturally they are very different, especially the elders. Not in a bad or negative way, just different. You'll learn all that.
Tuba City is really close to the Grand Canyon, Lake Powell, and Flagstaff, all incredible places. And the Painted Desert surrounding Tuba City is amazing, in a completely isolated, vast, remote kind of way. I love it out there. Much of the Navajo Reservation is incredibly beautiful red rock desert, and exploration is unlimited. Canyon De Chelly, Kayenta, Window Rock, Shiprock, all worthy places to visit. Mexican Hat and the San Juan River areas of southern Utah are close by, the bluffs and canyons of Kanab in Utah. Seriously, you'll be at the heart of the red rock desert areas, some of my favorite places on earth.