As a resident of South Florida, I have visited the Keys numerous times, and I agree with doing the trolley tour. It stops at all the places folks need to see, plus keeps you off your feet walking. The main street in Key West is Duval Street. That is where the action is with tourists and locals. So even if you decide to not take the trolley, Duval Street is where you want to be.
'Penny 3333' is absolutely right about the key lime pie...Blonde Giraffe is the best. More places on your 'have to stop in tour' are Sloppy Joes and Hogs Breath Saloon. The conch fritters at Sloopy's are the best I have ever had. Hands down. Both places sell t-shirts (little pricey) but worth it to say you've been there. See if there is a place called 'Pappy's' which is near Sloppy Joes. They have the most amazing fried shrimp....oh Lord!!!
One thing about the Keys: they are laid back. Its not about five minutes ago down there. People are very friendly and willing to help. I will not say there are no interesting people down there, but man, are they fun to watch. When you get off the ship, look for a local newspaper. It highlights all local hotspots that tourists don't know about. Hopefully, your ship does not leave until evening. The locals have a celebration at Mallory Aquare every night as the sun sets. Awesome!!