Civitavecchia/Rome If you just want to go to Rome, the best way is to take the train if not with a driver. There are several running all day. The trip time is about a little over an hour.
Livorno/Florence Livorno is very big and industrial; it’s a long walk to the port entrance. And Florence is about 1 1/2 hours away via auto/bus.
Montecarlo If you dock there, there is a water taxi that is about 5 minutes from the dock that takes you across the water to the foot of the town. It runs every half hour or so and is very inexpensive. But you then walk about 5 or 6 minutes to an escalator/elevator that takes you right up to the back of the casino and town.
Barcelona. I'd say it's about a 25 min walk to the main entrance of town depending where you’re docked. But I’d take a 5 min cab ride to monument a colon and from there it's about 5 min walk to the beginning of Las Ramblas.
Mallorca the port would be Palma. It’s about an hour walk into town.
Palermo. ship docks right downtown. You can walk into the center of town; 15-minute walk to the Quattro Canti. Cefalu is a pretty little town and well worth a visit. It's about 50 mins from Palermo.
Naples is notorius for traffic congestion. You dock in Naples. A walk to the train station is about 25 min.
Tunisia There is a train station not too far from the port (out the gate, turn left at the statue) which will take you to one end of downtown. But you should probably know some French or Arabic to do it. Two things that you are likely to want to see, the Medina and the Bardo Museum, which are across town from the port and probably requires a cab. The train going north from the port will take you to Carthage too.
I suggest taking a cab or ship shuttle to the old town, about a 15 min drive. You can take a ferry to Lokrum http://www.dubrovnik-guide.net/lokrum.htm
The ferry leaves every hour (every half hour in summer) and it took about 15 minutes. This is a beautiful island with swimming off the rocks, a swimming hole, old monastery which is now a restaurant. Make sure you leave plenty of time to get back to the ship because the traffic gets real bad and it can take a half hour or more to go just the few miles to the ship.
Corfu. You dock in the city but the "old" historic area is a long walk. I’d take a cab.
You can just walk around the town. There are two beaches in town. A long flat one with very shallow water to the right of the docks and a very small sandy one with chair rental on the left.
Santorini is DIY. I suggest taking the cable car from the tender pier to Fira, about 5 min or so. But you can also walk up 600 steps or ride the donkey. Cable car is more enjoyable though. Fira has a ton of shops and cafes. But everyone goes to Oia. We rented a car in Fira for $25 plus $7 for insurance. If you have the car you can drive to/from the beach and anywhere else on the island.
You can catch a cab/bus to Ephesusi about 45 minutes, but the price can vary. There’s a travel agent, Meander Travel just outside the port. They offer pretty good rates for a driver, guide, and entrance fees.
Valletta docks right downtown. If you want to go to the beach check either Riveria next to Golden bay, Ghadira or Paradis bay; all nice sandy beaches but they are on the northern part of the island around 30 min away from the port and the taxi might be expensive. You can always take the bus since the bus terminus is in Valletta.
Yon can walk from the port into the center of Valletta (uphill) and explore the city. You should take a taxi (or local bus) to the nearby Mdna (old town) section where you can see the interesting buildings and walls.
Messina Taormina is about 30 miles away which you can do on your own. It’s a good 15 min walk to the train station. If you don’t want to walk, you can catch a cab. It's really a nice train ride along the coast. Below is the link so you can get an idea of the times and fares.