We stayed at the state park, Anastasia state park and really liked it. Not sure of who is camping with you, children and all, but we took a segway tour from St. Augustine Segway Tours (I think) and loved it. A bit pricey, but worth every cent. About a two hour tour of the city. The guide asked us what we wanted to see. Our reply was: What's there to see, do, eat and where to park our RV. Just the DW & I and the guide and had a blast. Highly recommend it!
p.s. If you have a geezer pass the fort is free. That's also a nice thing to do.