Much of the action in Key West is concentrated in Old Town and around the seaport, which is good given that parking is so limited and pub crawling is a major tourist activity. Given the size of the island - 7.4 square miles - walking is the best way to get around town, but buses and taxis are available.
Key West is the perfect place to bicycle - no hills and far easier to park than a car. Bicycles can be rented through numerous outfits and some hotels and guest houses. Scooters are another option.
The city of Key West has four color-coded bus routes and two between Key West and Marathon. A one-way fare in the city is $2 or $8 for a one-week pass. Buses swing by infrequently though - every 60-90 minutes, service ending before midnight, but if you plan it right you can get to the airport for $2 instead of $20. Buses have bike racks. You can also travel to Key West from Miami by bus.
Florida Keys Dispatch, in business 40 years, is the first Florida taxi company to go hybrid. Its pink cabs, equipped with bike racks, charge $2.95 for the first 1/5th of a mile than, 70 cents for each 1/5 after that. It's at the Key West airport 24/7. There's also shuttle services from the Fort Lauderdale and Miami airports. Key West passed an ordinance outlawing Uber or other ride services.