Old Town is small enough to do entirely on foot or by bike, and the two things worth leaving it for are a fort at the end of the island and another one 70 miles out to sea.
Ernest Hemingway Home & Museum
907 Whitehead Street, open daily 9am–5pm, walk-in with guided tours included. Hemingway wrote here through the 1930s; the grounds are still home to six-toed cats descended from the one a ship's captain gave him. Allow an hour.
Fort Zachary Taylor Historic State Park
601 Howard England Way, open 8am to sundown every day of the year for $6 per vehicle; the fort itself closes at 5pm. A pre-Civil War National Historic Landmark holding the world's largest cache of Civil War armament, and attached to the best swimming beach on the island, with a café and chair, umbrella and snorkel rental. Re-enactors the third weekend of each month.
Harry S. Truman Little White House
111 Front Street, open daily 9:30am–5pm, guided tours from $24. Florida's only presidential museum: Truman spent 175 days here across 11 visits, Eisenhower recovered from his 1956 heart attack in the house, and Edison lived in it during the First World War.
Dry Tortugas National Park
Seven coral-and-sand islands almost 70 miles west of Key West, reached only by ferry or seaplane — a full day out, booked well in advance, with Fort Jefferson and clear-water snorkelling straight off the beach. Check the park's current-conditions page before you commit, as weather cancels trips.
Key West Butterfly & Nature Conservatory
1316 Duval Street at the quiet southern end, open 9am–5pm with last admission 4:30pm. A glass-domed tropical habitat with 50–60 butterfly species flying free, plus exotic birds and two flamingos. Tickets are sold online, and — rare for Key West — there is free parking behind the building.