There is a pretty good park over at jax beach on the end of penman next to the golfing range. Sometimes its a little muddy but usually people don't really take too aggressive of breeds there. Thats what i always worry about with my dog, hes a medium size mouthy doggie, and sometimes it gets him in trouble.
The one in Ponte Vedra is kinda sweet cuz it has a lake that they can swim in and a place to wash them off afterwards. But i cant really remember the location.