Check Florida City CG , Florida City .. city run place that will allow storage for a few $$'s a day.m Not a great place, but it works for storage. We have left our trailer there several times while riding the bike down to Key West. Another option is Southern Comfort CG in Homestead ( about 1 mile from Florida City CG).
You could look for a mini-storage facility nearby the port .. most will accommodate a trailer, just depends if they would be willing to do a week or so rental.
Once, I parked the trailer at Miami International Airport for a few days. They have an outside lot that accommodates trailers. Probably wasn't supposed to do it, but all was fine when I came back.
