Hi dickg and welcome to Cruise Chat.
What a wonderful trip you have in store! You'll love your floating resort.
You may want to check the Holland America web site
for a lot of information. Look at their Shore Excursion area. You can pull up excursions for each city you're visiting. If you scan the excursions, you'll see a few that jump out at you right away.
Any good guide book or online guide to the Greek Islands or the Med will have lots of information on your stops. Many volumes have been written about Rome alone!
There may be 3 "formal" dinners on a 10-night cruise, depending on the ship. Suit is fine for men, although some may be wearing a tuxedo. Women can wear a cocktail dress or dressy pants suit. Non-formal nights can be thought of as "going out to a restaurant" clothing.