Visiting in the late spring will help you find cheap hotels in Arizona, thanks to summer rates still generally held in effect. If you arrive in September, you can enjoy the Red Rocks Music Festival; remember you'll need to find hotels in Phoenix, AZ, since this is where the festival is held, but keep in mind there are many other great experiences around the state. If you visit Scottsdale, for instance, you'll get to enjoy cuisine in the city listed as America's second-best city for foodies.
Of course, you could seek out cheap flights to Arizona which land you near Mesa. This is especially ideal if you're visiting in December, since you'll get to see the Annual Mesa Arts Center Festival. Those arriving during the summer months might want to check out Oro Valley for the Oro Valley Concert Series.
If you're not big on finding plane tickets to Arizona based on random events, you could always check out the Phoenix Zoo, Papago Park, and gorgeous views of the Grand Canyon. Fortunately, there is no "off season" for these attractions. Make sure you book your vacation on Travelocity to ensure you have access to over 400 airlines and 510,000 hotels worldwide.