The Mediterranean (and European) ports of call tend to be less casual than ports in the New World. The attractions are more historical and cultural, too, with very few "beach" desitnations.. As a rule, the same sort of attire that you would wear on causal night aboard ship is appropriate for sightseeing and tours.
Some attractions have requirements for "acceptable" attire that are more strict than our customs here in the States. This is especially true of religious sites, such as churches and mosques. If you wish to visit these sites, you will have to conform to their requirements.
>> For gentlemen, a shirt with a collar, dress slacks, and dress shoes are pretty much acceptable anywhere during the day.
>> For ladies, a blouse that has sleeves, even if short, with either a skirt no higher than the knee or a pair of dress slacks. Most churches will require women to wear a hat or scarf on their heads, and mosques typically require women to cover their legs and their hair (but wraps for this purpose generally are available at no charge).
Hope this helps.