MSC provided a shuttle bus in to the old town which cost 7 Euros and was probably worth taking given the distance. The bus stopped beside one of the old fortresses in the heart of the old town and left plenty of free time to explore the town, the fortress, the views and pretty gardens if you wanted to. We found a small rocky beach with a swimming pier below the fortress. There was a very small charge to get in but there was a beach bar, changing facilities, showers and lifeguards / first aid.
The shuttle bus dropped me right in the centre of the old town and it was very easy to walk around the medieval city centre and the city walls to admire the gorgeous views of the town, the old churches and palace, the city gates, the old harbour and the sea. This busy tourist destination was very crowded in the centre and had endless shops and cafes many priced in both the local currency and euros. There were cash machines in the town if you wanted local currency.
We spent the day in the small port village of Katakolon. It was an easy stroll. There were plenty of shops selling souvenirs and arts and crafts and a good variety of tavernas, including some facing the sea front. It was a short walk to the beach where it was possible to swim, beach towels were provided by the ship on disembarkation.
There was a small but quite interesting museum of working models of ancient Greek inventions.
We didn't go in to town, we had a drink in a pleasant taverna a short walk from the dock (5 minutes across a busy road)
We visited Athens independently. We walked from the port to the train station in Pireaus which took at least 30 minutes but was a bit difficult to find. We had to ask directions more than once and it was very hot and tiresome! It would be worth getting a taxi to the Pireaus train station . The train from Pireaus into Athens was cheap and efficient and took us to the acropolis and main sights.
There were also plenty of taxis at the port offering taxi tours of Athens which might be worth considering for a large family or group.
Tenders land at the foot of the cliffs where there is a tiny harbour, a few shops and cafes and a pretty little church and fishing boats to look at. To get to the main town you can ascend the cliffs by donkey or funicular. There can be quite long queues so allow time to catch tender back to ship!
We took the MSC excursion to the Caldera. This was a boat trip to a nearby island where there was a walking trip to the top of a volcano (the whole of the archipelago of Santorini is the result of past volcanic activity) The island was very barren and rocky - wear sturdy shoes or trainers, not flip flops etc and take a bottle of water. There were small puffs of steam at the top of the volcano and good views throughout. The Greek guide was informative of the geology of the region. The excursion boat then anchored off another small island and we were able to swim in the sea from the boat. In a little bay near the shore there were hot springs which you could swim to (confident swimmers) and enjoy the experience of warm springs in the sea water and volcanic mud. The excursion boat had simple refreshments for sale and toilets. This was an enjoyable excursion worth considering if you have visited the towns on the main island previously and / or want to do something different. Cost 48 Euro.