Mandarin OrientalÂ’s new ultra-luxury Riviera Maya resort on the Yucatan peninsula is a secluded hideaway of individual villas and bungalows set in a private, 10ha (26acre) enclave tangled with mangroves and streams. Near by are numerous freshwater sinkholes and caverns offering swimming and snorkelling through underground rivers; and the astonishing Mayan ruins of Tulum. Although only half an hour from brash Cancun, this resort feels about as far away from the noisy, Texan-dominated holiday city as it is possible to get. Fly to Cancun on a cheap Â’nÂ’ cheerful direct charter, or on scheduled flights via the US.

Details: Seasons in Style (01244 202000, www.seasonsinstyle.com). A weekÂ’s stay costs {pound}2,490, including flights on American Airlines via Miami and private transfers.