The White Lotus is Mike White's HBO satire about rich people on holiday in a luxury resort, where a body turns up at the start of each season. This page covers season 2 in Sicily and season 3 in Thailand (season 1, in Hawaii, is left out). Both hotels that play the White Lotus are real and you can book them: San Domenico Palace in Taormina and the Four Seasons Resort Koh Samui.
In Sicily, stay in Taormina: the ancient theatre, Piazza IX Aprile and Isola Bella are a walk or a cable car away, and the Godfather villa and Catania's Teatro Massimo Bellini are an easy half day. Noto Cathedral and Cefalù Beach each need a full day. On Koh Samui, Anantara Bophut, Fisherman's Village and Choeng Mon Beach are close together on the north-east coast; Wat Phu Khao Thong and the Snake Farm fill a second day. The Bangla Boxing Stadium is in Phuket and the Mandarin Oriental in Bangkok, so plan them as separate trips.
Check before you go: the Godfather villa is private and opens only for booked tours, the temple has a dress code, and theatres, shows and the island reserve keep their own hours. Private villas used in the series (Quentin's house, Daphne's palazzo, the houses in Samui and Bangkok) are not listed.