I've done DIY scuba trip out of Key West. I've chartered sailboarts and a few years ago we brought our powerboat down from Chicago and kept it in a harbor. The trips were really easy to do. We stayed with the major dive sites, which are surrounded by mooring bouys. Just head to the site, hook up to an available bouy, and dive. Try not to get involved in anchoring. If one site looked crowded, we went someplace else. We own our own gear and rented tanks as we needed them. Get a good dive map with GPS coordinates at the major dive shops. (I assume you will take a REAL GPS with you if you are boating on the Ocean)
One MAJOR thing to consider is the size of the boat you are taking. I've done this with deep keel sailboats and with a 24" deep V powerboat. Some of the smaller, flats boats you see in the Keys will really get rocked offshore. You need to know the weather and the limitations of your boat, otherwise you can get in trouble really easily.