We are signed up for the tour that ends on Sunday April 13th, there are no activities scheduled, the tour ends after breakfast. We have a flight back to the states from Athens of Friday April 18th, and we think it best to be back in Athens the night before. Doesn't leave much time to explore other islands but we could peel off the tour a day early(which I am fine with, one of the people in our group less so). Santorini and Crete are the islands we are thinking. We want to hike the caldera. For Crete, we are not beach people but we do like hiking and sailing. I know we don't have much time but any recommendations on where to spend 4-5 days after the tour? I'll be tired of ruins and museums. Is there an island we can base ourselves that would let us do day trips to Santorini?
Not sure how you leave the tour a day early. You will be coming from Hydra and getting to Athens around noonish ( as I recall) so even if you go straight to the airport you won't get to whatever island you choose until late afternoon, giving you time to check in to a hotel and get dinner. ( which is unlikely to be as good as the Farewell dinner the tour has).
OR are you planning to leave Hydra after only one night and get back to Athens on your own?
No we were thinking of staying with the tour through Piraeus but going directly from Piraeus(skipping the Natl Arch Museum which we can go to the day before the tour starts) to the airport to which ever island we decide to go to first after the tour. I know trying to see two islands from Sun to Thursday is a stretch so looking for advice on which ones to most efficiently. I would be fine doing a day trip to Santorini. Plus it is the week before Easter so not sure what madness we will encounter. We are leaving Athens on Good Friday.
If you want to go to an island and do a day trip to Santorini, it is possible from the islands of Paros or Naxos.
See for example "Polos Tours" in Paros or "Zas Tours" in Naxos (there are others).
https://zastours.com/naxos-to-santorini-day-trips
https://polostoursparos.com/daily-cruises/santorini/
Paros and Naxos both have an airport and are also easily accessible by ferry from the port of Piraeus.
Naxos: https://www.visitgreece.gr/islands/cyclades/naxos/
Paros: https://www.visitgreece.gr/islands/cyclades/paros/
Be careful, Easter in Greece is a very busy time for flights and ferries