Itinerary Suggestions for Cyclades Trip in Sept. 2018

I've never been to Greece, but I can help with this part:

"Not sure of the domestic flight options out of Athens"

To find all flights from an airport, go to that airport's Wikipedia page (great trick I learned on this Forum). Here's the one for Athens: https://en.wikipedia.org/wiki/Athens_International_Airport#Passenger. It looks like Olympic has most, but not all, of the service to the Greek islands.

To find specific schedules, use Skyscanner to find all options: https://www.skyscanner.com/. Remember that all flights may not be daily, so you may have to jigger your itinerary to get it to work with available flights.

If you plug your travel dates into this website you will see which airlines are offering flights from Athens to whichever island you've chosen: http://tinyurl.com/y8vvbk5l

Lots of islands have airports: https://en.wikipedia.org/wiki/List_of_airports_in_Greece

Good for you. DIY in Greece is very easy.
My experience has been primarily on Naxos and Crete never been to Sifinos. While ferry hopping sounds great every hop easily eats up half a day so you have 9 days on the islands. The fewer hops you do the more time you will have on your chosen islands.

Naxos has an airport so is easy to reach from Athens. Aegean airlines which owns Olympic provides this service. This summer sky Express has also been servicing this route. So sign up for both web sites for promotional information. I was able to snag 4 flights from Naxos to Athens for under 150 euros total for 4 on an early season promotional fare. That promotion was in November 2016 for 2017 September travel. I love planning ahead. The airport is small so it can only be used by 50 seat turboprops. Flights book up early and when the seats are gone there won't be any more added later. Book early.

We have been to Greece 14 times and have stayed in Naxos a minimum of a week and a maximum of two weeks each time. We are still finding new things we never saw before on Naxos. I say that because you might want to consider just doing one island. Naxos can easily take up 9 days and you will never get bored.

In September I would consider staying at St George beach. Its part of Naxos town so you get a beach vacation with all the benefits of the activities of town. St George( Agios Georgios) is lined with small family owned hotels in every price range. Small sea view studios can be had for less than 60 euros a night. Hotel tip. Go to booking dot com and search Agios Georgios. It will give you availability price and reviews. Thats a good way to start to narrow down your choices. I normally just book right on that site but many people contact the hotel directly. Often even if the site say fully booked most hotels hold rooms for direct bookings. My rule of thumb is any rating 8 or above is going to be a good hotel.

Naxos has better beaches then St George but the beach/ town combination is a winner. When we feel like a full day on the beach we hop the KTEL bus and head west 7km to Plaka beach. Agia Anna and Prokopios are also nearby.

Naxos has a smattering of Antiquities and mountain villages where you can experience Greece like it used to be.

You can easily do day trips to Paros from Naxos on regular ferries. There is an excursion boat that goes to Santorini and on other days to Delos and Mykonos. Sometimes it a good idea to visit these famous islands without having to pay exorbitant prices for food and accommodation.
St George Beach Hotels Naxos http://www.flickr.com/photos/stanbr54/sets/72157632162394787/
St George Beach Naxos http://www.flickr.com/photos/stanbr54/sets/72157632113170279/
Plaka beach tavernas hotels https://www.flickr.com/photos/stanbr54/sets/72157655106193251
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
Naxos 2016 https://www.flickr.com/photos/stanbr54/albums/72157671589993576

If I read your post correctly you have a total of 11 days including 2 in Athens, leaving 9 for islands.

You can do 2 islands comfortably along as they are on the same ferry route and relatively close to one another.

Naxos as mentioned is a favorite for many, including me. You can combine Naxos and Paros easily with more time on Naxos than Paros. Both have airports so are quick and easy to get to. They both have ports for the ferry.

Sifnos and Milos are two more of my favorites with Milos having an airport and Sifnos just a port for the ferry. You can fly to Milos then ferry to Sifnos and ferry back to Athens. The ferry takes about 4 hours. Both islands are a more traditional atmosphere with nice beaches, villages, some archeological/historic sites and great food.

Two islands that most don't go to are Astypalea and Amorgos. Astypalea has an airport and you can ferry to Amorgos and ferry back to Athens. Unfortunately the ferry to Athens takes 9 hours but is broken up by stopping at 5 islands on the way back so you get to see the ports of several other islands.

Lots of options for accommodations depending on budget and needs, but September is off season with far lower prices and therefore more bang-for-your-buck.

I would suggest 6 nights on Naxos, on St. George's beach, and 3 nights on Amorgos, in the port of Katapola.

There's lots to do and see on Naxos and you can easily daytrip to Santorini and/or Mykonos/Delos. Do a search on this site for recommendations about Naxos.

Amorgos would give you a completely different experience. This small, beautiful island is easily reached via ferry from Naxos, and has very few tourists. We stayed at the wonderful Porto Katopola, for under 50 euros a night. This is a small pension with four rooms on the second floor that have huge balconies facing the port. I would snag those immediately since your group needs three of them. The friendly owner, Giannis, has other non-view rooms, but these are what you want. Incredible views. The rooms aren't fancy but are spotless and include a small kitchenette with hot plate and refrigerator. The price doesn't include breakfast, but last year when we were there he had an arrangement with a cafe down the street .... for 5 euros each we got HUGE breakfasts with eggs and bacon or yogurt, plus croissants, toast, cappuccino, juice. Delicious! There's a restaurant across the harbor called Almyriki that is noted for its fabulous spaghetti with lobster. Or just walk down the street to one of any number of restaurants for freshly caught fish. You can rent a car (or two) and explore the island. The most famous attraction is the Hozoviotissa Monastery built into the face of a mountain. There's a beach town (Aegiali) which we didn't visit; and the island's capital (Chora), very picturesque.

When you leave Amorgos, you can take the big Blue Star ferry all the way to Athens (9 hours) or get off in Naxos (about 3 hours) and catch a plane. (In May 2016 there was no Blue Star from Amorgos on Sundays, but other ferries could get you back to Naxos on Sundays. You'd want to check ferry schedules as part of your planning.)

We have been to several Cyclades islands (Milos, Sifnos, Antiparos, Paros, plus Santorini and Mykonos), and I think you would love the combination of Naxos and Amorgos.