Sunset Cay on the Folly River does allow live aboards, but then you will have to deal with the tidal river and the shifting sandbar right outside the marina, as well as a tricky inlet from the Ocean.
St Johns does also allow live aboards, but a couple of things you should be aware of are the river
current, the mosquitoes and narrow
dock spaces. Facilities are first rate, however, and do include a pool and gas pumps.
You could also try Mariner's Cay further up the Folly above Sunset Cay. They traditionally have not allowed live aboards as it is a 'dock-condo' development and the spaces are individually owned, but I think that they may be allowing live aboards on a case-by-case basis. You would need to contact the
dock master, Ed Geiger.
I have a slip at Mariner's Cay which I may be selling or
renting, so if they are open to the
live aboard idea please contact me if interested.