We were in Athens and Santorini in October about 2 years ago. It was not as warm or as dry as you might expect. I wore my Ahnu Montara boots with Sockwell compression socks for all daytime walking, museum visiting and hiking. I will call going to the Acropolis a form of hiking.
I usually switched to regular comfortable flats for walking to dinner, depending on the weather. I wore these Ahnu flats for that, but today I'd wear these Abeos.
The beaches on Santorini are not on the same side as the caldera/scenic side where most people stay. It's quite a walk over the hill, to and back from them, if you stay on the caldera side. There is a bus that you might be able to take. I'm not a beach person, but I'd guess the water will not be very warm.
In general, the islands start to slow down in October with the cooler and wetter weather and rougher seas. A lot will depend on when you are there.
I don't know what you mean by a "suitcase." Pack light and use a roller bag or backpack. We flew from Athens to Santorini and used fast ferries for all other island transportation. Arrival on Santorini was pretty dramatic for that Aegean plane. The wind and water was so rough that the Flying Cats and Sea Jets couldn't go as fast as they can when the seas are calmer.
And if you haven't been to Greece before, be aware that you typically don't flush used toilet paper down the toilet. You put it in a trash can next to the toilet.