Caymen Islands - slower pace of life, fairly wired for tax fraud purposes, easy to blend in due to British heritage
Miami Beach is pretty remote from the "real world" parts of the business-oriented United States - very little serious business going on here. Trust me, I live here! ;)
Another nearby option would be the Florida keys, which are pretty slow paced with lots of water sports. You can stay in a shitty hotel room and eat fish all the time, watching fearsome sea creatures out the window while working on your million dollar idea.
Also consider the Philippines, particularly Cebu. As an up and coming outsourcing powerhouse, Cebu is wired with highspeed internet connections, and it has nice beaches. My outsourcing team is located in Cebu City. Nearby Boracay is nice too, but the internet isn't as fast. A nice touch is that the main beach has WiFi if you want to work right on the beach.
And cheap. Very cheap. Let me know if you breeze through.