Haha, that is pretty interesting. Where in AZ are you heading? I started traveling about a year and a half after I became an Rn. A little over 1.5 years ago. I felt ready because the floor i worked on as staff was pretty difficult and after that experience, I felt like I was ready to tackle just about anything. I didn't have much trouble finding assignments at all. Some positions I wanted were filled, but it probably took me about a month to find a place to work after I started looking.
The best housing i've had in my two years of traveling was in L.A. It was actually in Downtown L.A, which is highly known for its business district as well as having an abundance of homeless people. However, i do think it was a safe area, and i, as well as the many other travelers that lived in the area never had an issue. The apartment was absolutely gorgeous. here's the link www.thepiero.com.
I'm not a big "across the country" driver, so for my first assignment, i shipped my car from boston to arizona (it was about $925, and i have never regretted doing this). My other assignments were in different parts of CA, so i ended up driving. Some companies do provide rentals, I would check ahead of time.
You are allowed to apply to multiple agencies. It is ok to be submitted to several hospitals by more then one agency. However, when you interview with a hospital and you choose to take that position, you are then committed to that hospital and that agency for whatever length of contract. Hope i answered your question.