I second (or third/forth/fifth) the motion for Key West.
Make sure you follow the coast both ways as it is orders of magnitude less bouncy than over land. Plus if you are lucky you'll get the magic clearance "at or below 500ft along the beach".
If you follow the Keys from Key Largo to Key West you'll see some fantastic scenery and there'll be a forced landing option (Hwy 1) that is more attractive than the sharks. Bring a camera!
I would recommend spending at least an evening in Key West as it's one of the few places in the US that seems to have character. The contrast from the horrible sprawl of Orlando is stark.
I believe I am correct in thinking this trip should cover the 300nm requirement if you make a pit stop somewhere around Miami, although I am prepared to be corrected by the ruler brigade.
Enjoy the trip.
Gareth.
P.S. My pics from my Key West trip:
Picasa Web Albums - Gareth