I'm heading down to Miami in May for work (yeah I know, life is tough!).

I do 24 hour mountain bike races and have one coming up the end of May, so I need to spend plenty of time on a bike...
I've been to Miami before and have no interest in mixing it up with the traffic. So, my Pelican cyclist friends, where in or near Miami can I ride? I'm willing to throw the bike into the rental car and drive somewhere reasonably safe. I'd take seperate bike paths, rails to trails, large parks etc. I can bring a road bike, a cyclocross bike or a mountain bike. Willing to take multiple loops of trails to add up some mileage.
Any suggestions? Thanks in advance. Also my handsome husband is coming down for a few days, what fun car or outdoors things are available in/around Miami?
angela