If you drive to Big Pine Key, you can walk the trails and look for the Key Deer. They are supposed to be quite friendly, although the 3 we saw ran away when we got too close. Close to there is Bahia Honda State Park, it has a nice beach and there are snorkel boat trips a few times a day. Book in advance to guarantee a spot, the boats do sell out. Both these are about a 45min drive from Key West.
As a previous poster mentioned, if you are driving down through the keys the drive is beautiful, and you'll probably want to stop along the way. Also, if you are into fishing, you can fish for free off dozens of bridges along the highway. We saw hundreds of people doing that. Even adding the cost of a license and fishing gear, you still save a LOT of money over doing a fishing charter. And many restaurants will cook your fish for you for $10-15.
I'd also recommend a sunset sail while in Key West. They take you past Mallory Square. Some are all inclusive booze cruises, while the cheaper (and more family friendly ones) are BYOB.
Finally, if you are driving from the Miami area, it's worth your time to spend a day in the Everglades (depending on the time of year you're going). The alligators alone are worth it! If you are flying into Key West then the drive would be too long for a day trip.