Returned from my second Med cruise June 13th. I wouldn't worry too much about dressing up. The main stipulation to get into the churches etc. is that your shoulders and knees are covered (no tank tops, mini skirts, or shorts). Comfortable slacks, loose-fitting long skirts, or capris are perfectly adequate.
As far as shoes go, the rule of thumb is to make sure they are comfortable. Many of the streets are cobblestone and it can be tough on the feet. The streets are also very dirty. The few times I wore thick sandals, my feet were filthy when I returned to the pensione. Lots of tourists wear tennis shoes or birenstocks..even in the Vatican. Save the nice stuff for the cruise.