Key West is easy to navigate by bike, but I agree with Alan that it's a small island. When you run out of land, there's a massive beautiful ocean to explore, you certainly won't get bored. There are tons of tourists year round, and many of them rent bikes & scooters, so you'll have plenty of two-wheeled company. Watch out for the drunks, the chickens, and you'll be fine if you can afford the absurd rent.

You can ride the entire chain of islands to the mainland, it's a popular tour route.