I am from Arizona and we have three Universities to chose from NAU wouldn't be that much different from where you are as it's in snow country - yes, arizona has a bunch of snow in parts of the state. ASU is my school and you may not see any snow but it is a bit warmer than where you are from. U of A is about 1500 feet higher and while still hot, the climate is a bit milder. If you want to be near a big city, ASU would be your school. For the smaller population center, consider the other two schools.
Outdoor activities vary between snow skiing, water skiing, hiking in the desert or tree filled mountains, fishing, floating down the river on a raft or inter tube or exploring the country away from the city. We have several native american indian tribes with a culture and history you may find interesting and a tourist industry the provides many interesting places to visit. If you want a state that offers pretty much everything within a few hours drive, you would have to look hard to find a state other than arizona.