I believe the navy dock is used when a third ship is in port. The two piers in front of the navy pier will be occupied first before the navy one is used becuase you have to be bused off the navy site.
If you can't walk far and want to see some sights then take the old town trolley and the walking to the sights you want should be short. Mallory Square has several sights right by it and LOTS of shopping...
2007 Victory & Triumph
2008 Conquest & Liberty
2009 Valor, Freedom, and Splendor
2010 Glory and Liberty
I agree with angel. There is a lot to do in Key West right by Mallory Square, where the trolley takes you. Within 1/2 block, there are enough museums, shops, restaraunts, etc. to keep anyone busy for a couple of days, if you so choose.