If you are going to be there only for a short time - up to 2 weeks, the Maricopa County Regional Parks are awesome - beautiful sites, trails and vegetation. Around Mesa would be Usery or McDowell Mountain. There's also Cave Creek and Lake Pleasant and White Tanks, depending what part of the greater Phoenix area you want to be.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel