This fascinating museum documents Columbus’ voyages and features exhibits on the Canary Islands’ historical role as a staging post for transatlantic shipping. Don’t miss the large section of model galleons (‘La Niña’) on the ground floor, which particularly impresses children with its working detail. The crucifix is said to have come from Columbus’ ship. In the next room are models of all three of Columbus’ ships: La Niña, La Pinta and the Santa María.

Rooms five and six contain historical maps and facsimiles of ancient maps, many from the early 16th century. Look out for the facsimile of the ‘Universalis Cosmographia’ map by the German cartographer Martin Waldseemüller, which was conceived in 1507 and is staggeringly accurate for its time. Astrolabes are also on display.

A large collection of artwork dwells upstairs, as well as a diorama of old Las Palmas with buttons for illuminating specific buildings and edifices. After descending the long stairs into the basement you are rewarded with displays on ancient South American pottery and history.

The building is a superb example of Canarian architecture, built around two lovely balconied patios, complete with fountains, palm trees and colourful macaws (the last make for excellent photo ops, but watch out, they can peck). The exterior is a work of art itself, with some showy plateresque (silversmith-like) elements, combined with traditional heavy wooden balconies.

Although called Columbus’ House (it’s possible he stopped here in 1492), most of what you see dates from the time this building was the opulent residence of Las Palmas’ early governors.

The spiritual heart of the city, this brooding, grey cathedral was begun in the early 15th century, soon after the Spanish conquest, but took 350 years to complete. The neoclassical facade contrasts with the sunlight-through-stained-glass-dappled interior, which is a fine example of what some art historians have named Atlantic Gothic, with lofty columns that seem to mimic the palm trees outside. You can also admire several paintings by Juan de Miranda, the Canary Islands’ most-respected 18th-century artist.

Your entry ticket also includes admission to the sacred art museum, set on two levels around the Patio de los Naranjos. The collection is a fairly standard array of religious art and memorabilia, including centuries-old manuscripts, wooden sculptures, sacred art and other ornaments, but the setting is lovely – and fragrant with the scent of orange blossom in springtime.

Once you’ve explored within, take the lift to the top of the bell tower for a stunning wide-angle view of the surrounding city and coast.

Beyond the cathedral is an expansive and good-looking plaza, which provides a dramatic setting for highly photogenic images of the entirety of the church facade against the (usually) blue sky.

These fabulous dunes cover 400 hectares and were designated a nature reserve in the 1990s, ensuring that the rapidly multiplying hotels would never encroach on their golden grains. The best view of the dunes is from the bottom of Avenida Tirajana: stroll through the arches of the Hotel Riu Palace Maspalomas to the balcony, which is surrounded by a botanical garden displaying shrubs and plants native to the Canaries. There’s a small information office here too (open 10am to 1pm Monday to Friday).

You can also get down to the sands by taking the lane just east of Hotel Riu Palace Maspalomas and walking down to the dunes. Do respect the sands and don’t litter, so you leave the environment as you found it. Alternatively, go the full Sahara and opt for a camel trip with Camello Safari. A note to photographers (and social-media users): come to the dunes towards sunset for the very best light conditions and photographs (as long as the weather is clear).

Don’t miss this museum (also called the ‘treasure house’), accessed upstairs from the rear of the basilica, where you can get a real close-up view of the Virgin and see the armfuls of unusual items gifted by the devout. There’s also a room displaying the outfits she’s worn through the ages (a new dress is premiered each year during the fiesta held in her honour) – however, the standout image is of the Virgin herself, with child, set upon a brilliantly burnished silver throne.

One of several viewpoints in town, the Mirador de Unamuno looks out onto a sweeping panorama of the vast volcanic caldera beyond – it is a stupefying sight.

The fine 3km stretch of yellow sand is magnificent, and is considered by many to be one of the world’s best city beaches. There’s an attractive seaside promenade – the Paseo de las Canteras – which allows walkers, cyclists and joggers to enjoy the entire length of the beach free from traffic. Perhaps the most marvellous part, though, is the reef, known as La Barra, which in low tide turns the waters of Las Canteras into a giant salty swimming pool that’s perfect for snorkelling.

Further south, the restaurants and hotels peter out and the waves become a little bigger. It is here, near the auditorium in an area known as La Cicer, that surfers congregate in the water and footballers take to the sand.

The extraordinary, neo-Gothic church stands sullen watch over the bright, white houses of Arucas in a striking display of disproportion and contrast. The church has a Sagrada Familia (Gaudí) look with elaborate pointed spires and was, fittingly, designed by a Catalan architect. Construction started in 1909 on the site of a former ermita (chapel) and was completed 70 years later. Treasures within include a nude, a reclining image of Christ carved by local sculptor Manolo Ramos and three magnificent rose windows.

Due to its huge size, the church is generally referred to as a catedral (cathedral).

These terraced municipal gardens are laid out in French style with fountains, pavilions, sculptures and tropical trees, including the rare evergreen soap bark tree (Quillaja saponaria) and several magnificent dragon palm trees, as well as some astonishing flowering plants and groves of gentle bamboo. Note the elaborate system of irrigation channels and water courses built into the park.

Calle Heredad flanks the garden on the southern side of the plaza, dominated by the beautiful neoclassical Heredad de Aguas de Arucas y Firgas building, completed in 1908 and now housing the local water board.

The greenish-grey stone cross from which this spot takes its name marks the centre of Gran Canaria and its historic caminos reales (king’s highways), along which it is still possible to cross the entire island. The site is one of the most popular coach-tour destinations with the resorts, so is usually swarming with tourists (hence the souvenir stalls and donkey rides).

From the lookouts here you can survey and contemplate the island’s greatest natural wonders: to the west is the sacred mountain Roque Bentayga and, in clear weather, the towering volcanic pyramid of Teide on neighbouring Tenerife is visible; to the southeast rises the island’s highest peak, Pozo de las Nieves, and the extraordinary emblem of the island, Roque Nublo (often enveloped in cloud). Dropping away to the northeast is Vega de San Mateo.

Walks of all levels extend from here, from half-hour strolls on paved paths to five-hour treks through the mountains. The 12.5km circular route from Cruz de Tejeda to Roque Nublo is especially recommended. Allow about 3½ hours and take warm clothing, no matter how hot the day might seem. You can get information and tips from the Hotel Rural El Refugio or the tourist office next to the large, free car park at Cruz de Tejeda. There are a couple of very touristy restaurants in Cruz de Tejeda. For a more exclusive dining experience, try the Parador de Cruz de Tejeda.