This is a very nice property!
I have stayed at all on Key West and I have found I do not need a car unless I go North from Key West.
The Marriott is a good ride and I think having a car is a terrible idea, especially if you are planning on having a few drinks. I have taken the shuttle and enjoyed it.
Do not forget to try Louie's BackYard for cocktails. I do not like to eat there but the locals make the beach lounge a real place of interest. The sunset there is the best!
We are planning to stay at the Key West Beachside resort in March. The hotel has recently implemented a $17 per day parking fee and rental cars are more expensive in Key West than other Florida destinations. Therefore, we plan to rent a car only for the weekend we arrive (to buy groceries and supplies). After that, we will rely on the free hotel shuttle to Duval St. Our upgraded room includes a full kitchen.