If "past" ST. Augustine means to the south; then, I think the next place that fits your description would be Halifax
Marina in Daytona Beach. Further south is New Smyrna Beach City Marina, but I don't think they have room now. Titusville usually has space and fits your criteria. There's Harbortown Marina on the canal
connecting the ICW
to Port Canaveral. Vero Beach has a good rate for their moorings if you can settle in a place without a slip.
If "past" St, Augustine means to the north; then there's much available in Jacksonville's Ortega River or in Brunswick, Ga.