Just got back from Eastern Med cruise and loved Dubrovnik.
I took a cab each time from the port to the old town. Holland America wanted $15 per person round trip; the cab was 10 Euros for entire cab (we got 4 people in it) each way, a much better deal.
DEFINATELY walk the wall. I think it cost 8 Euros and took over an hour to walk, If it's hot (it was 100o+), bring water and a hat!
I agree with the other poster: Visit the synagogue.