Just moved to Mesa at the end of last year. So far been to Cowtown and Ft. Adobe. Both about an hours drive from Mesa. I MUCH prefer the recball field at Cowtown to Ft. Adobe, and prefer the grounds (much more cover from sunlight available). Ft. Adobe does have better speedball fields.
Hoping to try out some other fields in the area, but I don't think there are any other outdoor fields from what I've read.