The closest beach with Deep Sea tours is about an hour away from Orlando. near Port Canaveral and Cocoa Beach.
Some links are
http://www.captbobfishing.com/
http://www.irishjigfishing.com/
http://www.fishobsession.com/ - has private and Party Boats
There are a ton more here:
Yahoo Results
Private charters are of course more expensive and greatly improves your chances of landing "The Big one" where Party boats cram as many people as they can on a boat for a lot less and everyone has lines out along the boat and things get tangled. Here in North Florida we call the Party Boats vomit cruises because when one spews everybody spews.
Let me know how it goes.