looking for historic lodging

On Santorini both Aspa Villas and Olympic Villas offer traditional cavehouses that are nowhere near as expensive as a luxury hotel.

Beware that most of the buildings on Santorini have been rebuilt after a huge earthquake in 1956 destroyed much of the island villages, so you may not find anything "old and historic" on the island.

https://nauingreece.blog/2015/06/19/devastation-of-the-1956-earthquake/

You'll have better luck finding "Old and Historic" on an island like Crete, especially Chania. Besides Crete is a lot better than Santorini, especially in October.

Nafplio would be another excellent option with beautiful architecture, especially the Old Town.

Lesvos is another great option, especially Molyvos with it's beautiful Old Town cascading down the hillside toward the waterfront.

Lots of option other than over-the-top Santorini.

On my trips to Greece, I never experienced any historic lodging, but I also based many decisions on price. If you do get to Rhodes, I see http://www.marcopolomansion.gr/ recommended on a couple of different sites, such as this Hotel Guru, found purely through a Google search.

It's far from comprehensive but you might find a relevant tip in newspaper articles such as this for Crete: https://www.theguardian.com/travel/2014/jul/23/crete-greek-island-holiday-guide or this other random "Secret Greece" site.

Cave houses,ugh! We stayed in a very expense cave room on Santorini, dark, damp. Upgraded to a larger one, still too dark, damp. I would avoid them at all costs!
And the earthquake on Santorini in more recent years caused many places to slide down the cliffs.

In the 34 years that I've been going to Santorini there has not been even one incident of any cavehouse "sliding down the cliffs".

Thank you for your responses. I know that Santorini is tourisy but we really want to visit Akrotiri. I wish we could get to Rhodes but it is too far from everywhere else we will be going.

sarahzm - I guess, then, it’s “The Rhodes Less Travelled.” We’re heading just to Crete in October - hope you have a great trip.

We stayed in Napflio last year beneath the old Palamidi Fortress, but at Rick Steves’ favorite Pension Marianna.

We changed rooms in a cave house hotel trying to get away from the dampness and darkness. We couldn't. We would never stay in a cave room again.

For sure stay in a cave house. The contouring shape of the cave inside the houses are really cute and unique. We had zero dampness, the AC worked great, it had an amazing view right below the famous 3 domes. the walkways were hosed down every morning and it was super clean. it was a very unique stay. you will enjoy it. the pools are awesome as well.