Just about any range should let you shoot a shotgun. I shoot mine at the (somewhat) local indoor pistol range (Shooting Sports, Tampa). They typically ask that you don't use a far right or left lane, so the eventual spread doesn't scar the wall. But otherwise, I've shot buck and bird shot without any problems.
The following link will show you a lot of ranges in FL. Just give the range a call to make sure it's okay first. Since you mention NE, I'm assuming the Jacksonville area?
Gateway Rifle & Pistol Club is one that comes to mind. If you are far enough north, try searching for Georgia as well, you just might find something close there too.
http://www.nrahq.org/shooting/shooti...l.cgi?state=FL
Happy shooting,
LL