What started out as being set on a Rick Steves' Greece Tour has morphed into self-planning, mainly to have more island experiences. For a trip of approximately two weeks, what would be the most appropriate bases to consider; We are very active, enjoy history, hiking, swimming, eating, and drinking. We are also planning this visit in the spring/early summer. We would like to experience as much as possible without poorly considered travel issues.
Consider Athens, Napflio and a few islands. If you go to Santorini, give it less time than other islands. See the caldera view and Akrotiri , then leave. Islands with a much more Greek feel are Paros, Naxos and basically all the others with exception of Santorini or Mykonos.
Based on my research planning our trip for last May, if you are interested in the islands, it is easier to stay within the Cyclades regarding traveling from one island to another.
There are so many wonderful islands for you to visit. You should do your own research to see what appeals to you, but I can certainly give some suggestions. The guidebooks I used are Lonely Planet, Michelin Green Guide, and Fodors Greek Islands.
We loved Santorini! Yes, it is crowded but I think it is worth it to see at least once in your lifetime. The caldera views are stunning but there is more to see in Santorini than just the caldera. If you go, I recommend 3 nights; rent a car for one of the days so you can travel around the island and visit the Akrotiri archaeological site, the Akrotiri lighthouse, red sand beach, black sand beach, etc.
From Santorini, you can easily travel to Naxos via the Blue Star Ferry. It's a 2-hour ferry ride. Naxos is very different from Santorini. It's quieter and more laid back. We spent 4 nights here and rented a car for a day to travel around the island. That was one of the best days of our trip.
If you want more islands, from Naxos you can take the ferry to Paros and Antiparos. We didn't have time to go there but there are Greek experts on this board who know a lot about these islands and more.
If you want a varied experience, I recommend visiting the Peloponnese Peninsula and stay in Nafplion. You can visit lots of amazing ruins from here. You can fly from Naxos to Athens and pick up your rental car. It's a 2-hour drive to Nafplion.
And then end your visit in Athens.
How many destinations you include depends on how many nights you have on the ground. Our trip was for 16 nights, and we visited Santorini, Naxos, Nafplion, and Athens.
I am sure that Janet and Stanbc will respond, along with others who know more than I do.
As others have suggested, you want to stay within one island group for ease of traveling. Many first time visitors focus on the Cyclades but there are many other choices.
I would suggest that you fly to your first island upon arrival and save Athens for last. With two weeks, I would be thinking of four bases. We had two islands (Santorini and Naxos), Nafplio, and Athens. Friends of ours followed same route but visited Meteora instead of Nafplio. Others have visited Paros or Milos. You are spoiled for choices (and these islands are all in the Cyclades).
Greek is wonderful! You can’t visit it all in one trip so just make choices that work for you.
As you have decided to do self-planning, you are going to have research and preparation work and you will realize that there are many more choices than what RS offers.
With 2 weeks you can go to 2 or 3 islands, only 2 would be more reasonable.
May-June is an excellent time to go to the islands, the daylight last longer, the vegetation is in bloom, all accommodation, restaurants, etc. are open, there are a lot fewer people, the beaches are quiet (but the sea can be a bit chilly). And the prices are lower.
For 3 couples, I advise you to find a villa, a Cycladic house or an apartment with 3 bedrooms.
You will be much more independent and free than in a hotel and it will be much more pleasant (and certainly less expensive)
To speak only of the Cyclades which represent less than 15% of the Greek islands, and which therefore far from being the only possible choice, here are some examples of pairs of islands that are well connected to each other. With the exception of Milos which has an airport, they are only accessible by ferry.
Milos and Kimolos
Serifos & Sifnos
https://www.visitgreece.gr/islands/cyclades/sifnos/
Amorgos & Koufonissia
https://www.amorgos-island.gr/en/
http://www.koufonisia.gr/?lang=en
Sikinos & Folegandros
https://www.visitgreece.gr/islands/cyclades/sikinos/
I know all of these islands but I'm not Rick Steves and and I don't like to tell people "I've been there, so that's where you have to go", so I'll let you do your homework.
That said, you still have time
The first time we were planning to go Greece, I asked my Greek friend which islands to visit. and she told me there are many island groups but six major ones. The Cyclades are only one of those groups. It is easier to stay within one group of islands.