Welcome to Fleming Island -- I love it here as well!
I've visited a number of shops in the area (on the other side of the St Johns). You will see some of the "same old same old", but you'll also find some unique pieces:
Tin City Antiques, 11740 San Jose Blvd
Tin City Antique Mall | Jacksonville, Florida
Avonlea Antique Mall, 8101 Phillips Highway
Welcome to Avonlea Antique Mall
San Jose Antique Mall, 5107 San Jose Blvd
San Jose Antique Mall - 2916 University Blvd W. - Jacksonville FL - 32217
And here's a site with a list of many others:
Antiques - Jacksonville, Florida
As for art that's unique to the south, there's nothing more Floridian than Highwaymen art. I'm searching for a piece myself - not cheap, and real ones aren't easy to find.
This site has info about the art: Art About Florida - Highwaymen - James Gibson (broken link)
Every first Wednesday of the month is the Art Walk downtown. There are many talented local artists (and .. um .. some not so talented), and the galleries are open with no admission from 5 to 8. The Museum of Contemporary Art (MOCA) is also open and free during the Art Walk.
Again, a hearty welcome to our fair part of The Sunshine State!