On formal nights most men wear tuxedoss or dark suits (you will see a few white dinner jaskets as well). Most women wear formal or cocktail dresses and lots of 'baubles'.
Research your ports before you go (internet). You can do many things on your own, just make sure you are back to the ship on time; you don't want to see it sail without you.You can usually get taxis or obtain excursions right at the dock. In addition to the booked shore excursions offered in your Adventures Ashore booklet, Princess provides general port info. the night before you get there.