Though it is a bit of a drive back to the east coast of Florida, it would certainly be worth your time to visit Dewings Fly & Gun Shop in West Palm. http://www.dewings.com/

They have more in the way of high end field guns than clay guns, but it is still a great spot to shop and worth the trip.

As to places to shoot, check out your area on:
http://www.wheretoshoot.org/Find_Range/index.asp