I recently found out there was a dog park here at Caesar Chavez park. It located south of the skate park and if you drive by you'd never think it was there. It probably under a year old. There is parking on the east side of the dog park.
They have two areas: one area for big dogs and one area for little dogs. I'm still trying to find a time when a lot of people bring their dogs so I can take my dogs to play with. It seems like Saturday about noon is a good time. We were there today and there were at least 10 dogs there at one time which I thought was really cool.