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If Krios doesn't work out why not follow the E4 path 1.5 km or so to the next beach called Viena? The walk over hill takes about 45 min and quite enjoyable if it is not too hot (it is not recommended to walk in the middle of the day). This is quite interesting with some old marble columns from a collapsed temple lying in the sand. The beach is fairly small comprising several small bays of rocks, sand and stones. You will probably only be disturbed by the occasional walker making their way to Elafonisi or back.
2016 June: Still a good prospect. The small bay pictured below has room for 3 or 4 couples and is perfect for nudism.
2020 September: the small bay was visited by people (clothed) with boats who put up a tent and left it there. Plenty of room in the other bays. End of the season, mostly Greek people, all nude.
alanrp42
It’s interesting to see the archaeological remains here although the remains of the marble pillars lying on the beach are being slowly eroded away. There’s a relaxed attitude to nudity and if some clothed people appear they are unlikely to be fazed by it. The part of the E4 path from the Western part of Krios beach is quite steep with loose rocks and you may prefer to bypass this part by going the longer way on the dirt road instead.