Greece

When you arrive at the port, you will find numerous taxis just waiting to whisk you anywhere on the island. The island is small and it doesn't take long to get anywhere. There are easy & convenient local buses between Oia and Fira. Walking the streets of Oia is fun although you might very well encounter wall-to-wall people. The streets are very narrow and Oia is very popular.

Sometimes it's best to take the tour's excursion if offered because of time restraints. There are taxis available in Athens and on Santorini to take you to Oia or wherever you choose to go. The Sigalas Winery in Oia has award-winning wines but there's not much to see. It's not like a French chateau/winery. On Mykonos you can take a shuttle van or taxi to the dock where the boat to Delos departs. Closed Mondays. Departure: 10.00am
Return (there are 3 boats): 12:30 / 13:30 / 15:00 Boats leave from old in-town harbor jetty, behind town hall.

By far the quickest way from Piraeus to the center of Athens is on the metro green line, which takes only 15 min. to Monastiraki and costs only E1.00. You avoid all the traffic congestion this way. It's about a 20 min. downhill walk from the cruise port to the metro station, easily spotted on the map facing the harbor. We took a bus #40 or #49 last time because we had bags with us.

In Santorini, I think you would want to take whatever excursion necessary from RC that would get you into Oia or Fira. It's not a flat island, where you land at the dock and can just walk into town. Our friends went to Santorini on a cruise ship, and did not take the ships's excursion, and regretted that decision. The ship allowed all passengers who had booked ship excursions to get off the ship first. They got into a little boat, that took them to the shore. By the time our friends got off the ship, and waited for transportation once they arrived on land, several hours had passed, as there were several cruise ships in port and taxis were limited. Santorini was one of the stops they had looked forward to the most, and they barely had any time on the island. We were not impressed with the winery on Santorini; I think your time on the island could be better spent just admiring the amazing view. I think you can easily manage Athens and Mykonos on your own. Delos is well worth a visit.

Thanks so much for all of your replies. They are really helpful. sounds like we need to take the RC excursions for most of the trip or else we don't get off the ship fast enough.