This is a great dog park for folks in Tempe who want a nicer offering than the smaller off-leash areas within the parks near downtown (like the one on 5th just west of Mill and the other park in the older neighborhood nearby south of University). I normally drive all the way down to Chapparal Dog Park, but Papago is just as scenic and clean--only a bit smaller.
Most all of the owners have a good handle on their dogs--you will get a full mix of sizes and there is usually only one enclosed area open at any given time. There is a parking lot near the playground nearby but I prefer just leaving my car on the street as it is a shorter distance to the park and my dog is less distracted by the kids running around.
Finding this place can be a bit tricky, but if you're coming from Mill, drive east on Curry and then take a right on College (south). If you're coming from Rural/Scottsdale Road, go west on Curry and take a left on college (park is on the right hand side). The dog drinking fountains are pretty weak, so bring water or a bowl. Also, my dog gets pretty dirty here as it tends to be muddy in some areas.