You've got good advice in here.
I'm a St. Aug Native currently 'on hiatus' in Chicago.
Know the town like the back of my hand. When I was in high school, used to MD in all the historic places that today would probably get you arrested, save for the fort grounds. Always knew better than to try that caper, but I was tempted and had it all planned it out in my mind
Even got to MD the Lighthouse grounds around the Keepers House, when a relative worked there. Now, trying that would probably result in the SWAT team getting called out.
Beach detecting St. Aug is like beach detecting most anywhere else. You're gunning for the same 'lost' stuff. Ever since the renourishment, the 'old stuff' is buried too deep. You have to walk damn near 3 miles north down the island, through the state park to the inlet to get where there's still virgin, non-renourished beach. I hit that area this Christmas- random clad from the 70's-early 90's and junk. A couple encrusted objects I didn't bother to clean, but I only worked the dry.
Going out after big storms can be productive in terms of interesting artifacts. There *are* wrecks out there. As a kid, we used to play on St. Aug Beach and gather up handfuls of dime-sized fragments of white and blue shipwreck pottery (English, I think?), then just leave it there because no one cared about it at that time. Here's an ancient wooden shipwreck timber with iron spikes my mom found after a storm.
As far as the touristy stuff, can't give much good advice on that since after ya live around it for so long, it ceases being relevant- but the Fort is a must, a walk to the top of the lighthouse is underrated and the Alligator Farm is cool. Anastasia State Park is nice if you like nature'y stuff (Used to ride my bike in there and MD the intercoastal beaches all the time with my ancient Whites Coinmaster hastily semi-waterproofed with rubber cement, electrical tape and a coating of black spraypaint

. Again, didn't know I wasn't supposed to, but no one cared. Things are way different today... and sadly, it isn't like I'm "old")
Man, do I ever miss home.