Unfortunately, South Beach is one of the least dog friendly areas in the whole city. South beach park is between 2nd and 3rd Streets and Brannan and Bryant, but other than that I can't think of another park other than a small one at King and 2nd. Bernal Height is a good dog area and anywhere closer to the Golden Gate park is good, too. At Fourth Street and Berry there is decent place to walk your dog right along the canal. There are others, but why don't you run a google map search and zoom in so you can see the green spaces.