John:
You picked a great place in Florida to stay! The closest Dive shops to you are Deep Six Stuart and Deep Six Jensen. As others have said, charter boats operate out of Jupiter and Palm Beach and go out every day of the week, weather permitting. I try to lead two trips a month: one for beginners and one trip geared towards advanced divers/ spearfishermen.
If charters aren't your thing, the Treasure Coast has tons of great shore diving sites ranging from 10-300 yards from shore; the only catch is visibility The Gulf Stream is a little further from shore in the Martin/St. Lucie area so vis is more hit or miss then Palm Beach. The best places for diving/snorkeling from shore in Stuart are House of Refuge, Fletcher Beach, Bathtub (closed) and any other beach access along McArthur Blvd. There is also an old wreck (Gorges Valentine) just south of House of Refuge. Further north, the outside reef at Jensen Beach Public is nice, but a little far offshore:200-300 yards. Ft Pierce State park has the best developed reef lines in the area with some ledges 5-10'+ deep.
If you have access to a boat, the area affectionately known as Peck's Lake just south of St. Lucie inlet is a great place to catch lobster (no spearing or fish collecting).
For more local information and any other questions, feel free to call either Deep Six Location.
Deep Six Jensen
3317 NW Main Ave Jensen beach
772-692-2747
Deep Six Stuart
2791 SE Martin Square Corp Pwky
772-288-3999
Steve W
Deep Six Jensen