Yes, I have stayed in the Navy Lodge there. You can walk to the Exchange, a beach bar / restaurant, boat / jet ski rentals and fishing charters. We loved it and would stay again. Just down the road at the air station,there are also nice CBQ rooms. You would need transportation from either ocation to the downtown area, but we had no problem with taxis.
I live in Gov't Housing right across the street from the Fly Navy Bldg in Key West. I personally would stay there if it was just my wife and I and its a easy taxi to the down town area or you can walk(I walk it's only 20 min)I can give you lots more info but I don't know what you really want to do while your in town. E-mail me at CGScotty@comcast.net and we can talk more. There are lots of variables to go over. EM1