Sikinos island

I spent 2 nights in Sikinos a few years ago in May,
If you are looking for calm and tranquility, you will have it!
If you are looking for the authenticity of the Cyclades you will have it too. You will also have
opportunities for hiking, going to deserted beaches and seeing countless small chapels.

The big problem with Sikinos is figuring out how to get there. This is also why there are few people there.

In Sikinos, no Blue Star Ferry, no Seajets.

From Athens the two ferries that go to Sikinos are the Artemis from Hellenic Seaways and the Dionisios Solomos from Zante Ferries.

You can take the Artemis from Milos or from the port of Lavrio in Athens.

The crossing time from Athens - Sikinos is approximately 10 hours.
After Sikinos it continues towards Santorini, which means that the next day it leaves Santorini for Piraeus via Sikinos.
The Santorini Sikinos trip takes only 2 hours

Zante Ferries timetables are not yet published for September (won't be until July I think) but you can always get an idea
by going to:

https://zanteferries.gr/en/timetables-from-piraeus-to-western-cyclades/

You will see the schedules until the end of July. Those for September should be similar.

If you have at least a week to spend in quiet, less touristy islands, you might consider this course:

1/ Go to Kimolos and stay there for a few days.
Kimolos is an island easily accessible from Milos. You can take a ferry or a flight Athens-Milos
From Milos (port of Pollonia) there is a ferry that leaves several times a day for Kimolos

2/ Catch the Dionisios Solomos on the way to go to Sikinos. Stay in Sikinos for a few days

3/ From Sikinos still by ferry, go to Santorini.

4/ Take a return flight from Santorini to Athens

You can do this trip in reverse starting with an Athens-Santorini flight

If your plan incluldes a to visit Santorini you have 2 options to reach Sikinos. The Zante ferry leaves from Athinios but stops at Riva on Thirassia as well, so if you are staying in Oia you can take the morning shuttle ferry from Amoudi Bay below Oia across to Riva instead of having to go all the way to Athinios. This is what I did and it was so much more convenient than having to get to Athinios. But the Zante ferry is not a daily ferry, so make sure you have up-to-date departure times.

The Zante ferry leaves from Athinios but stops at Riva on Thirassia as
well

Zante Ferries no longer stops at Riva (Thirassia), maybe not enough passengers to disembark or embark