Do a web search for South Florida kayaking, but here are some to get
you started:

http://www.atlanticcoastkayak.com/trips/trips.htm lists places such as
Cayo Costa, Ft. Myers; Matheson Hammock, Coral Gables; Deerfield
Island, Deerfield Beach; New River, Fort Lauderdale; Fisheating Creek,
Palmdale; Nine Mile Pond, Flamingo; Florida Keys, Islamorada/Key
Largo; Rookery Bay, Naples; Cypress Creek, Pompano Beach; St. Lucie
Estuary, St. Lucie; Lake Okeechobee, Lake Harbor; Turner River, Big
Cypress Preserve; Loxahatchee River, Jupiter; Whiskey Creek, Dania
Beach.

There are also others such as Quiet Waters park in Deerfield Beach and
Westlake Park in Hollywood ... not to mention the Intracoastal, of
course.

I don't know where you can store your kayak, though, sorry.

Welcome to South Florida! Don't forget the sunscreen!!