Certainly, this is one of the rare gems of the island and everyone should tour the museum at least once. Give yourself a good amount of time, so do not go when you have margaritas on the brain. Early in the morning is a good time, as the sun shines over the water on to the Fort. You can walk right there to, as there is a sidewalk ride along the waterfront that goes for miles. Next to the museum is a small park, by the Airport, for picnics with a view.
You cannot miss this exhibit, which highlights so much about what Key West went through as part of its childhood. A red brick fort seems so odd, and that is the way it was built. The memorabilia is outstanding to view and learn about, making your brain even more loaded than ever with Keys facts and tidbits.
We do almost everything on our bicycles when traveling on land down here, even when we go to Stock Island. Some of the better attractions are Mel Fisher maritime - Solares Hill (fast bike ride down) - West Martello Tower - Key West Lighthouse - Key West Cemetery - Western Union Schooner - Audubon House - and the Truman Little White House, which is in the Annex. The fence is only locked at night, so you can bicycle around the area during the day with no problem.