Not real close, but a couple of places come to mind. One is Fort DeSoto, a Pinellas County park with a campground on the Gulf at the base of Tampa Bay. Be sure to book the dog section.
Another waterfront option on the Gulf is at Turtle Beach, a Sarasota County park and small campground. A bit pricey and hard to get a res.
Another is Oscar Scherer State Park just south of Sarasota, though not waterfront. Lots to do in the area...the beaches are close, there's kayaking at the park, the Ringling Museum, Mote Marine Lab, much more.
