Costa is very efficient at arranging tender transfers. The lift is really the only way to reach the town, we came down on foot but a would not recommend it unless your pretty fit, the path is slippery at all times, particularly where the donkeys are tethered. Walking around the town is enjoyable but can be crowded when there are a number of ships in.
We wanted to travel independently so researched all the bus and train options which were thwarted when no bus tickets were available at any of the news kiosks. We took a local cab into Athens (20€) and negotiated a pick up with the driver, who proved totally reliable. Another stroke of luck was the fact it was a public holiday and a large march planned in Athens, with many roads closed. Quite surreal driving into Athens on an almost empty motorway. Additionally, entry to the Acropolis and the museum was free for this day.
Only in the port a short time so took the tender and walked around the Main Street. There were 4 ships in that day so plenty of people adding to the atmosphere. Some interesting shops and lovely waterside restaurants to while away the time. The duty free shop on the way back to the tenders was one of the cheapest we found.
Much has already been written about this port and Rome itself, but here are my tips: 1. After taking the free port shuttle, turn right ont of the gate and walk 400m to the railway station 2. Don't join the queues for the ticket booths, but go to the speedy ticket machine (10€) return, takes around 35 - 40 minutes 3. Get off the train at the Vatican station, St Peter, it will save a further 15-20min travelling into Rome Termini