You will be plagued by taxi drivers as you walk out of the Terminal Building. Don't accept the first offer, just keep walking & they will get cheaper every stride you take. They will wait for you to take you back to the ship so agree the price for the whole trip. Good Luck!
Be very very street wise in Naples pickpockets /bag snatchers are a big problem don't put your money in one pocket/bag don't wear expensive watches jewellery and if you shop at a market stall haggle and check that what you have bought is correct before you leave they are very good at substituting inferior goods when see there hands.
You can get there and back by train - very much cheaper than a taxi.
Walk out of the port and you can catch a tram to the railway station. you buy the tickets in the newsagent just across the road. Catch the train to Pompeii.(Pompeii scavi?)Think it's about 5 euros. Take bottled water as it will be hot in August. We went in Sept.You can have a guide to walk round with you or do your own thing.If you are OAPs show your passports and you get in free or certainly at reduced price. Allow at least 2 hours to see it all. Same train goes to Sorrento. Some say it is possible to do both but it would be a rush.We actually came back on the bus. Same price just different scenery.Bus drops back closer to the port unless you catch the tram.
Watch crossing road when come off ship .drivers dont stop allso watch them on mopeds in case they mount pavment nock you down or snatch your bag even if sitting at cafe dont lay bag on table in case they just come bye and snatch it .enjoy your cruis.