If you manage to catch your limit with some time to kill, one thing you might want to check out is the Key's very own ghost town, known as Indian Key. At one point in time this island was the county seat for Monroe County, but now it is a State Park. Along with Key West, the island was the only part of the keys to remain populated during the Second Seminole War. That is, until the Seminole Indians staged a raid of the island and massacred 13 of the residents while forcing the other 50 or so people to flee the island.
There is not a whole lot to do on Indian Key, but it has an interesting history and there are still some remnants left from the people who lived there. There is a nice boat dock and a lookout tower provided by the park service, but I don't remember there being a whole lot else. I do remember it being really hot, with not much shade on the walking paths. Its a tiny island and only takes a short time to explore, so if you happen to be boating by with some time to kill be sure to check it out.
While you are there, try to guess what the "deep opening" is in the town square... because thanks to this placard we know that the Florida Park System has no idea. Hey, at least they're honest.