Greece and Italy using Euro , do not wait to change money in Europe and for sure not in Italy as money exchanger will give you very bad rates. Change or while you still in the US or check you ATM/CC rate for using it abroad. In Italy most of the places accept CC (Visa and Master card are widely accepted AE less) in Greece the big resturants and shops will accept CC. For a 7 week cruise in Europe I bring around 300-400 Euros mainly for taxi from to the airports and for street food rest CC. On the worse case scenario there is one ATM on the ship that dispense Euros bit with 6.5 $ fees
Cheapest rates are almost always to be had from withdrawing euros directly from an ATM once in the EU. Use euros in the ports; on board you can use dollars, for instance the casino is dollars only and I wouldn’t hesitate to tip in dollars if more convenient for you.
Fyi if you need to break euros on board you can do so at guest services
