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You can certainly do Carthage by yourself. There are plenty of taxis when you leave the ship. Just remember to agree a price before hand. We paid 60 Euros recently for a taxi to take us to La Marsa, Sidi Bou Said, and Carthage, and the driver waited for us. We are sure we could paid an even lower fare if we had bothered to haggle. Carthage is really worth a visit.
Pompeii is very easy to do yourselves without the need to book a shore excursion.The train from Naples which heads for Sorrento stops right outside the entrance gate to the archeological site. It is very easy to listen in to guides by stopping near to a group; there are also numerouse guide books for sale outside. To economise even further, download and print out information on Pompeii before leaving home. Another nearby site of equal interest is Herculaneum, which is the next stop after Pompeii on the same train route. This site has much more infrastructure to see, including the original port.
We paid for an oganised trip to both (one trip)and really enjoyed it. I think it depends if you want an easy time of it or trying to save money.
Pompeii is very easy to get to from Naples, use the local line, a bit basic but it stops right at the entrance. Take good walking shoes as those old stones are hard. Also take an umbrella, either for shade or for rain.
Pompeii is awesome.You could spend a whole day here but run the risk of missing the ship as traffic is horrific.Take a tour and get a good running commentry.
We had an organised trip to pompeii,we were disappointed with the time allowed there you need at least a day.Then we found out that we were close to the ship and a taxi would have been reasonable.We also wanted to go to Herculanium but no time.I think if you researched it you could do it yourselves very easily. gai.
Not know about Carthage but Pompeii from Naples is easy by train and a lot cheaper, also you get more time to appreciate Pompeii without being dragged around with a crowd.
You can walk from the ship to the train station soaking in Naples as you mingle with life there. Passing some brilliant shoe shops!! Takes about 20 mins. Then catch a local train to pompeii ensure you get off at the correct pompeii stop there are 2 one after each other - can't remember which is the right one. Wander around pompeii then back to train station & back to Naples or south to Sorrento for a quick wander around this fascinating Italian city and then catch a fast ferry back to Naples - stops right next to the ship.Enjoy beiong an explorer and don't pay through the nose for expensive ship excursions. We have done this twice and intend to do it again in Sept.