I'm no expert on St Aug, but I do live in the area.
The official oversized parking area is here
29.898389, -81.318972
It's the one others have previously mentioned off Castillo Dr. Large enough for the biggest of charter buses, etc... and I don't think I've ever seen it full, except maybe when they have an occasional festival in the field there.
Sadly it's a bit of a walk, but not too far. It's always struck me that the city of St Aug doesn't go all out to welcome RV'ers.
Anyway, the Visitor's info center is on the opposite side of the parking garage form here. From there, you can get the tourist trolley rides, etc..
I'm not aware of anything better close to the old town area....but at 23ft you might be a bit more likely to find on-street parking maybe (?)
When we go there by car, if we don't get into one of the close lots we'll usually find street parking somewhere with the several block area of this neighborhood. 29.895623, -81.315900
Not sure if that would work for you, but maybe at 23ft....
Additionally, there is a county ordinance against parking overnight anywhere...no walmarts, etc...
If you can get in, Anastasia State Park is nearby and is a very popular campground. Others nearby that I know of
a private CG over on Vilano Beach (I've never stayed there but have heard good things)
Stagecoach RV Park is a private place out by the outlet malls and the highway. Lots of permanent or long term folks there, but it looks nice enough I suppose. (I've never stayed there but have driven through a couple times for a look)
Cooksey's RV park closer to town, lots of permanent residents & does not look nice to me, but it's probably an option.
and there's a KOA out on St Aug beach