I really like Hance Dog Park. It's about as far from me as Steele Indian Park is, and I much prefer this one. It's maintained well, and they usually close the park if there's much rain to preserve it. I like that there is a good amount of seating around the dog park, and there are bags and trash cans all around the perimeter as well. No excuse not to clean up after your pup! I've never encountered an aggressive dog here either. There's always a good mix of dogs here that play well.
Bonus: if you come in the evening you get a decent view of the sunset and Phoenix skyline.