I like Steele Indian School Dog Park, particularly when viewed within the larger context of the Steele Indian School Park. It's a great place to take your dogs for a walk around the park and then let them loose for a run in the fenced area. The dog park has all the essentials: Fence. Bags. Water. Shade. Picnic benches. Some grass.
A suggestion about parking. You can park in any of the Steele parking lots and walk to the north and east to find the dog facility. If you're not in a mood for walking, the only entrance to the dog park parking lot is found off of Seventh Street (just north of the VA Hospital). I didn't even know there was a Seventh Street entrance to Steele until I searched for it.
There are separate areas for small dogs and large dogs. While admittedly not based on a large number of visits, the small dog area seems a lot busier. Perhaps an urban park frequented mainly by small urban apartment dogs or just my bad luck. Don't know. Still, the large dog area is busy enough weekdays after 5:00 and on weekends.
The Friends of Hance Dog Park, another a City of Phoenix facility, is located nearby if you are looking for alternatives.