If you've been hankering for a trip to another dimension but have yet to find a portal, the House of Eternal Return by Meow Wolf could be the place for you. The premise here is quite ingenious: visitors get to explore a recreated Victorian house for clues related to the disappearance of a Californian family, following a narrative that leads deeper into fragmented bits of a multiverse (often via secret passages), all of which are unique, interactive art installations.

Created by the Santa Fe art collective Meow Wolf in an old bowling alley (donated by Game of Thrones author George RR Martin), the space is large enough that you could spend several hours here – or visits – trying to crack the code to the safe at the top of the stairs, reading every detail of Mom's diary or finding inspiration yourself in the makerspace at the entrance. Weekend nights see live-music shows at the heart of this compelling imaginary world.

For more than 400 years, the Plaza has stood at the heart of Santa Fe. Originally it marked the far northern end of the Camino Real from Mexico; later, it was the goal for wagons heading west along the Santa Fe Trail. Today, this grassy square is peopled by tourists wandering from museum to margarita, food vendors, skateboarding kids and street musicians. Beneath the portico of the Palace of the Governors, along its northern side, Native Americans sell jewelry and pottery.

This top-quality museum sets out to trace the origins and history of the various Native American peoples of the entire Southwest, and explain and illuminate their widely differing cultural traditions. Pueblo, Navajo and Apache interviewees describe the contemporary realities each group now faces, while a truly superb collection of ceramics, modern and ancient, is complemented by stimulating temporary displays.

With 10 beautifully lit galleries in a rambling 20th-century adobe, this museum boasts the world's largest collection of O'Keeffe’s work. She’s best known for her luminous New Mexican landscapes, but the changing exhibitions here range through her entire career, from her early years through to her time at Ghost Ranch. Major museums worldwide own her most famous canvases, so you may not see familiar paintings, but you’re sure to be bowled over by the thick brushwork and transcendent colors on show.

The oldest public building in the US, this low-slung adobe complex began as home to New Mexico’s first Spanish governor in 1610. It was occupied by Pueblo Indians following their revolt in 1680, and after 1846 became the seat of the US Territory’s earliest governors. During research the Palace was undergoing renovations; expect a new look after its scheduled 2020 reopening. The adjoining New Mexico History Museum engagingly tells the story of the state, beginning with the Spanish arrival in the 1500s.

Santa Fe’s French-born bishop Jean-Baptiste Lamy – hero of Willa Cather's Death Comes for the Archbishop – set about building this cathedral in 1869. Its Romanesque exterior might seem more suited to Europe than the Wild West, but the Hispanic altarpiece inside lends a real New Mexican flavor. A side chapel holds a diminutive Madonna statue that was taken into exile following the Pueblo Revolt, and has been known since the Spaniards’ triumphant return in 1692 as La Conquistadora.

New Mexico’s State Capitol, informally known as the Roundhouse, was laid out in the shape of the state symbol – also the emblem of Zia Pueblo – in 1966. Home to the state legislature, which sits for 60 days in even-numbered years and just 30 in odd years, it holds one of the finest (free) art collections in New Mexico. Visitors must check-in with the information desk first. Pick up or download the free self-guided tour pamphlet.

Built in 1878 for the Sisters of Loretto, this tiny Gothic chapel is famous as the site of St Joseph's Miraculous Staircase, a spiraling and apparently unsupported wooden staircase added by a mysterious young carpenter who vanished without giving the astonished nuns his name. The chapel is no longer consecrated and can be rented for (nondenominational) weddings.