I've never camped there (my folks have lived there for half the year for 20 years, so we stay with them)...you should know that there's really no "beach" there. It's surrounded by water, but the shores are waveless and rocky. The closest you'll get is at Ft Zachary Taylor state park near the Truman annex. Its beautiful with great snorkeling, so you should check it out.
Best restaurants: el sibonney for Cuban, hogfish, rusty anchor, half shell raw bar, mangrove mamas about 10 miles before you cross the bridge, and baba Lou's is good.
Have fun...I'll be down in December!