Advice on a few days for the islands

If you're looking for relaxing, I would definitely recommend Hydra.

Its about 90 minute ferry from Piraeus, where the more famous Cyclades will be 6-10 hours. Hydra has no cars. There is the town spreading around the harbour, and hikes or water taxis to the beaches around the island. To be fair, these are not white sandy beaches, but a bit pebblier. Look up Rick's videos on it.

We can recommend the Pensione Alkionides for accommodations; and Xeri Elia Douskos, the best restaurant we ate at anywhere in Greece.

Hydra has rocky not sandy beaches and I think the Rick Steve’s tour goes there already.

We chose Naxos for its sandy beaches as a stop on our two trip to Greece. Ironically, there were so many other things to see and do we only spent a few hours on the beach!

I have heard that Milos has wonderful beaches but that you really need to rent a car. We did rent a car for part of our stay in Naxos but would not have had to as there is decent public transportation.

Your choices for travel are flying or ferry. We ferried to Naxos from another island and then flew back to Athens.

What other islands did you go to Beth? Did you fly to the first island or ferry? I am looking for something fairly easy to get to. I wonder if any coastal areas on the mainland would be a good way to end the trip?

Thank you Darren. We do spend two nights on Hydra with the tour, so I guess we would want to look at a different area that is easy to get to. Any other suggestions?

In October, I wanted a relaxing, low key experience and went to the Greek isles. After a week on Crete (no beaches in walking distance from Chania or Heraklion) I went to Santorini, then Naxos by ferry, and flew from Naxos to Athens for a few days.

In mid-October the tourist season is winding down on most of the islands, but it sure didn't feel that way on Santorini. The crowds were off-putting, the towns (Fira and Oia) were very touristy and I didn't want to rent a car to explore the "good parts." On the other hand, Naxos was exactly what I had in mind. I had a small apartment on St. George beach, walked to the center, took a day tour of the island, and chilled. The flight to Athens was fast and easy. The Naxos airport is tiny, 30 minutes is all you need before the flight and it's a short drive from town. From the airport I took the bus to downtown Athens.

The earlier you go in September the more crowded the islands will be. However, it's probably better to spend your first days relaxing, then fly to Athens for the tour. And you'll want to be in Athens the night before your flight home. I encourage you to allow at least 2 days in Athens in addition to the tour. There's a lot to see in the city that's not included in the tour.

Lots of islands to suggest with what you are looking for. I would recommend going after the tour since the later part of Sept will find tourism winding down so you will not have to deal with lots of tourists.

Where to go is subjective. With 3-5 days it may be difficult to combine 2 islands unless they are close to each other.

I have been to a number of islands that could possibly appeal to you.

Tinos (A Gem!)

Sifnos (Our first Greek Island)

Milos (Beautiful geological formations/beaches)

Naxos (I hear it's getting more tourism as people are looking for alternatives to Santorini/Mykonos)

Amorgos (Lovely!)

Crete (Large with more than enough to keep you occupied for weeks)

Chios (Beautiful and filled with wonders)

Lesvos (Home of my ancestors and something for everyone)

Ikaria (If you love free-spirited locals with a touch of anarchy you'll fit in!)

Others I have on my "to-go-to" list or worth considering:

Kythira
Aegina & combine with Agistri
Lemnos
Karpathos

Lots of options so check out this website for Greek Islands and see if there is an island(s) for you:

https://www.greecetravel.com/greek-islands/

We flew to Santorini, ferried to Naxos, and then flew back to Athens. We spent 3 nights on Santorini and 4 on Naxos.

If you decide you want to go to Chania I just wanted to state that from Chanias west wall at Talos Square, the town beach is a 10 minute stroll along a tree lined waterfront street at Neo Chora.
Here is Chania
Chania https://www.flickr.com/photos/stanbr54/albums/72157632117917828

Naxos is lovely and will give you a great experience. You should consider flying to and from whatever island you choose. With so little time its much more efficient to fly than to ferry.
Naxos
Trip around Naxos

http://www.flickr.com/photos/stanbr54/sets/72157634605629689/

Naxos trip 2019 https://www.flickr.com/photos/stanbr54/albums/72157711294807761

Thank you all for the great suggestions. Naxos might be a good option. Thank you Chani for the information about the Naxos airport and how crowded Santorini was. I definitely don't want that. Thank you Tommy for your suggestions. I will check out the website and look at the options you suggested. Stan, thank you for sharing your awesome pictures. They are inspiring! We do have to make our island time after the tour, and I think that will work out well to end the trip with some relaxation.

Have a great time.
There is a good chance you will be planning your next Greek trip on the flight back home.