Two we used were 'Salt Run' where you come in the inlet, and turn south. You will see a ton of masts with a good anchorage. There is a dingy landing near the light house, where we spent a couple nights.
The other one is south of the Municipal Marina. They charge for dockage, but it was worth it. You get water
, showers, trash disposal for a reasonable daily charge (don't try to tie up without paying... someone here did and complained loudly about how they got their dingy locked up for a little thing like not paying the listed fee...
You may see some boats anchored off of the fort (north of the Bridge of Lions). There seems to be a trend to do this, but we observed lots of bucking and passed on that one.
St. Aug was a really nice place to stop, lots to do and see. Enjoy! We sure did.
OBTW, there is a mooring
field planned, but nothing has been done with it as of the last time I checked... I am sure others will post updates.