Best dog runs (with parking nearby)?

We're moving to Greenwood Heights from a little farther north, and one of my goals for this summer/year was to get my dog back to the dog run more regularly. Our new area (on 4th ave) seems to have loads of parking, so I thought maybe coming and going at any hour won't pose a threat to not finding another spot. And since I have a car, why not pop my dog in it and drive to a dog run in southern Brooklyn? So I was wondering which dog runs (looks like the choices are Owl's Head and Dyker Beach, but also I could drive up to McGlorick or McCarren, there's usually ok parking around there, too, am I missing any others?) dog owners felt were the safest, best and knew there was a pretty good selection of parking around the perimeter of the park. My dog is 32lbs, gets a little snippy with new dogs (warning growling/snapping), but is good with small and medium sized dogs. I'd like to find a park that isn't too crowded, nor too aggressive, that we can go to several times a week. Thanks!