Chandler Air Service would be my recommendation. Good fleet of PA28 and C172 for rental at competitive prices.
Send them an email with any questions (preferably that you can't find answers to yourself from this site or google). If you haven't already, you'll need to get the ball rolling with obtaining a US Pilot Certificate based on your UK PPL. To do this
click this link to the FAA website and follow the instructions.
You should easily be able to do 50-75 hours of flying inside 3 weeks, and there is plenty to do and see in Arizona. You can fly up to (and across) the Grand Canyon, land at Sedona and visit a variety of other interesting places.
