Most of mainland SE Florida doesn't work in west winds. It is offshore, excessively gusty and hard to keep your kite flying. You typically end up drifting offshore with your kite on the surface, not readily relaunchable. Don't kite offshore winds here in short.
Your best bet for that wind direction would be to arrange for a sea taxi to the Miami Flats if you can through ASM or Miami Kiteboarding. The Flats are close to 7 miles offshore and west winds typically are fine out there. An alternative would be to arrange for a sea taxi out of Islamorada with the Otherside or Sevensports to the Florida Bay Flats.
You are in luck, there is the Ski Rixen cable center at Quiet Waters Park in Deerfield Beach, FL.
http://www.skirixenusa.com/