You won't find many places that will accept the dollar, except for banks. For incidental purchases, tips, etc. ashore your best bet is to get Euros from an ATM. Stores and restaurants will generally accept Visa or MC.
We purchased a "tip pack" from AAA before leaving. It was about 40 euros in coins and small bills. But we still had to hit an ATM in Naples.
We cruised on the Gem in the Med last October, from Dover to Barcelona. It was fantastic.