I have been fortunate enough to be able to go to the Florida Keys several times over the years. On many of those occasions I have booked a day fishing trip with Gulfstream Key West. They run a large party boat operation and provide all of the necessary fishing gear. The prices are reasonable at about $65, plus rod rental and fish cleaning.
They take you well off the coast to an area where you WILL catch fish. I have never gone with them and not caught several fish, but of course it is still fishing and not catching. We've caught everything from grunts and snappers to small sharks when I've been aboard. The crew has always been very helpful with getting set up and figuring out what we've just caught. They will also clean your fish for a small fee and tell you where you can get your fish cooked.
The best part about fishing with these guys is that you could be staying at a hotel or wherever and you don't have to worry about bringing any fishing gear. They have the rods, bait, filet knives, snacks and drinks. It is also kid friendly! Of course there is always the chance that you may get sea sick, so prepare yourself with Dramamine if you don't know.
If you are ever in the Keys and you have the itch to go fishing but didn't bring any gear, go check these guys out.