There's no place in Florida or on the east coast to my knowledge with consistent wind. Some places and times are more probable though. The Keys seem to have more consistent winds than most other parts of Florida however. There are two sides to the Keys, the Straits of Florida side bounded by shallower water out to the reef tract with deepwater beyond. Then there is the Florida Bay side with extensive shallows followed by the Gulf of Mexico. If you are far enough offshore in either area, you can ride winds from all directions. In the case of Florida Bay, you will likely have shallow water and sand bars, i.e. good butter conditions accessible by boat in most cases. Various operations in Key West and Islamorada will take you out there for kiting. On the Straits side typically you do better with winds that are side onshore to onshore. Given that the Keys are curved, the actual compass directions correlated to this will change as you move down the island chain. To get far enough from shore to escape most land effects on the Straits side, you will have some waves in a number of cases, so it is best to choose directions that are less sensitive to them. Most of the very few shoreside "beach" launches in the Keys open to the Straits side.
The point of this explanation is that most of the Keys are quite similar in terms of riding quality once you are out there. Getting there usually means departing from Key West or more recently Islamorada I understand. Given that the best riding can be offshore, the concept of one launch being better than the next loses some meaning unlike conventional mainland kite beaches.
So, you might plan on visiting The Kitehouse in Key West for a run to the Flats and if they are online with backcountry trips, think they must be, hit the new shop in Islamorada, Otherside Boardsports Shop . These two operations can also fill you in on the limited shoreside launches and related restrictions. You can also find out quite a bit by searching for Keys on this website. There is more info and links to these operations in the Guide to Florida at:
http://fksa.org/forumdisplay.php?f=42