I agree with IslandCruz and Penny3333. You can walk it, but when we go there, we take the trolley.
I haven't been there in a while, but if I'm not mistaken security checks your ID on the way back into the port area.
Carnival Fascination 12/2001, Triumph-5/2003--11/2/2008
Glory-9/2004 -- 10/2006 --9/2007 -- Victory-7/2006,
Costa Atlantica 2/2002-- 2/2005----Magica 2/2006
HAL MS Zuiderdam 9/03
MS Zaandam 1/04
Sun Princess 9/05
Royal Caribbean :
Majesty of the Seas 11/01
Sovereign of the Seas 12/02
MSC Orchestra 1/09
Ru** Princess 10/09
Yes, they always check your ID and ship card to get in the port area. I was a little younger when I walked this distance, and it was in the upper 90's. Not to mention I went to the cemetery first. I actually made it part of the way back. Those drinks along the way eventually kick in.
You can get a free map at the Conch Train station.
In the late spring,the summer and the early fall you will find the humidity to feel oppressive in Key West -if you aren't used to it! Other times of year a walking tour isn't bad at all (unless your out of shape or not used to doing a lot of walking. As Dwayne has referenced for you- the Conch Train (Trolley) is always a great option.
The Old Town Trolley - cousin to the Conch Train has on off privilege and Southern Most point is a stop. It will be a pretty good walk though from where the ship docks. I also will agree that depending on when you go, the humidity is enough to make you just want to give up and go back the the ship! We were just there on 9/22 and we did a six block walk that did me in ... we settled for lunch and drinks at Hogs Breath Saloon...service wasn't very good and the food was just OK but at least I got to sit down!