Places to Wear Thong Swimwear. If you like wearing thong swimwear, but don't like conspicuously being the only man or woman on the beach in a thong, then you should try these beaches. Agia Napa. See on Google Maps. We have heard that Agia Napa is the Blackpool/Ibiza of Cyprus and not to be tried unless you are a clubber type in your 20's!