In the 1960s, the Mexican government used a computer to choose the site for a major new resort in the Yucatán, the thumb-shaped peninsula that protrudes into the Gulf of Mexico and the Caribbean Sea. It came up with the current location of Cancún. Since then, the eastern coast of the Yucatán, including, from north to south, Cancún, Playa del Carmen, Cozumel and Tulum, has become one of the busiest tourist destinations in the Western Hemisphere. However, the Yucatán can still be a superb destination for travelers in search of tranquility and unspoiled natural beauty, as well as fascinating Mayan archaeological sites. On a recent trip, we focused on places that have yet to attract cruise ships or chain hotels, beginning with a few days on Isla Holbox and then continuing to the charming colonial cities of Valladolid and Mérida.

Located off the northern tip of the Yucatán and reached by ferry from the town of Chiquila, Isla Holbox is a narrow, 26-mile-long island in the Yum Balam Flora and Fauna Protection Area (which is internationally famous for the whale sharks that migrate there each summer and fall). The word “holbox” means “black hole” in Mayan, but the color that defines Holbox today is azure, the hue of the warm, shallow waters that lap its palm-shaded beaches of fine white sand. For now, easygoing Holbox (pronounced ole-bosch) is a barefoot paradise where casual clothing and suntan lotion are all you need for a low-key vacation. It is on the cusp of becoming better known, however, as reports of its beauty are spreading rapidly by word-of-mouth. So now is the time to go to Holbox, especially if you regret not having visited once-beautiful Tulum before it became overrun.

From the airport in Cancún, it’s a two-hour road transfer to the sleepy little port of Chiquila, where you embark for the 25-minute crossing. (Light aircraft flights from Cancún are also available and take 35 minutes.) Holbox’s sandy lanes are lined by thatch-roofed whitewashed houses and plied by electric golf carts, the primary means of transportation, along with bicycles, on this almost entirely car-free island. You may have trouble getting a signal on your phone. Likewise, internet access at all of the island’s hotels is spotty. Initially, this can be frustrating, but soon you realize it’s extremely therapeutic to be offline for a few days and that the world can wait while you enjoy another tamarind margarita or get lost in a novel you finally have time to read.