Zante
We spent a few days in Zante in 2018, not too far from Alykes. I can verify that Gerakas Beach, Vrontonero Beach and the extreme eastern end of Crystal Beach see nude use and are worth checking out. I also visited a small quiet area near Alikanas called Agriosikia Cave on capnbarefoot.info, not a beach at all but OK for catching some rays if time is short. FWIW, one day we rented a boat and took it to Shipwreck Beach; we only witnessed a couple of small beaches between Alykes and Agios Nikolaos with any nudity (and Laparda, listed on Captain Barefoot, wasn't one of them). BTW you could also check nakedplaces.net for more info.
If (like us) you like the freedom that a rental vehicle offers, be sure to get an International Driving Permit (IDP) before you leave home. Without one, rental companies in Greece will not even rent you a scooter over 49cc, let alone a car. That's a serious impediment unless you intend to mostly stay close to your hotel.