Arizona hunting questions

I just received news that I will be going on a business trip to the Tucson area for a little while. I don't have to work weekends, so instead of sitting in my hotel room, I figured I'd bring my Marauder and do some hunting. I have a few questions before I plan my trip. Do you need a license to hunt collared doves and jack rabbits? I know some states don't require a hunting license to hunt pests. My second question is where can I hunt? Is there any state land within an hour drive or so of the Tucson area? I do plan on going to AoA while I'm there, so hopefully they can help me out a little. My boss loves the excitement I have for this trip, I just don't have the heart to tell him it's not because of work :) Any suggestions on where to go and what to look for would be greatly appreciated.