Spend a night in a cave house in Guadix's Barrio de Santiago, where about 2,000 cave houses hold around 3,000 residents and stay at a constant 18°C

Climb to the Alcazaba, the Moorish fortress above Guadix, which surrendered to Ferdinand and Isabella in 1489

Around two thousand cave houses in Guadix hold roughly three thousand people, and they are not a curiosity — they are ordinary homes, dug into soft clay hillsides, whitewashed, with chimneys sticking out of the ground above them and a constant internal temperature of about 18°C whatever the season. In a place that reaches 40°C in summer and freezes in winter, that is simply the best available engineering. Several are let as accommodation, so you can spend a night underground and find out.

Guadix: A Night in a Cave House

Go to the archaeological museum and the necropolis and work out what was found here on 21 July 1971

Work out what the cavity in her side contained and what that makes the sculpture

Find out where the original is now and how long Baza has been asking for her back

Come in September for the Cascamorras and find out what happens to the man who runs it

Find the Arab baths in the old Jewish quarter, which are among the best preserved in Spain

On 21 July 1971 the archaeologist Francisco José Presedo Velo found a 4th-century BC Iberian sculpture in the Cerro del Santuario necropolis of ancient Basti — a seated woman in polychromed limestone, carved by the Bastetani, with a cavity in the side that held cremated remains. The Lady of Baza is one of the defining objects of Iberian art, alongside the Lady of Elche. The original is in Madrid and the argument about returning her to Baza has been running for decades. The town also holds the Cascamorras, in which a man tries to seize an image and is covered in oil for trying.

Baza: The Lady in the Museum

Ski or snowboard the Sierra Nevada Ski Station, Europe's southernmost ski resort, on 115km of pistes between Pradollano (2,100m) and 3,300m on the slopes of Veleta

Ski the runs that hosted the FIS Alpine World Ski Championships in 1996

Drive the A-395 from Granada, 27km up to Pradollano; the season runs from late November to early May

Sierra Nevada is the southernmost ski resort in Europe, on the slopes of Veleta above Granada, running from 2,100 metres up to about 3,300 — high enough to hold snow into May at a latitude further south than Tunis. It hosted the Alpine World Ski Championships in 1996. The thing people do with it that they cannot do anywhere else is ski in the morning and be on a Mediterranean beach in the afternoon, because the coast is about seventy kilometres away.

Sierra Nevada: Skiing Europe's Southernmost Slopes

Drive the mountain road from the Pradollano ski resort into the Sierra Nevada National Park — the paved road climbs above 2800m on the approach to the observatory, offering an unobstructed southern horizon above the Mediterranean

Visit the Observatorio de Sierra Nevada at 2896m on a public open day — run by the Instituto de Astrofísica de Andalucía since 1962, with optical and infrared telescopes

Summit Mulhacén (3479m), the highest peak in mainland Spain, and photograph the coast of Africa on the southern horizon on a clear morning

A Class 1 IDA dark sky designation covers the summit area of Spain's highest mountain range — the Sierra Nevada Observatory at 2896m sits on the approach to Pico Veleta (3398m), the second highest peak in mainland Spain

The Sierra Nevada Observatory and Mulhacén

Go into a secadero and work out that altitude, not technique, is what makes this ham possible

Taste a ham cured for two years against one cured for a year and find the difference

Walk the three barrios stacked up the slope — Alto, Medio and Bajo

Work out the climb: 190 metres from the Barrio Bajo to the Barrio Alto, whose highest house is at 1,610 metres

Walk up towards Mulhacén from here, which is the standard approach to the highest peak in mainland Spain

Trevélez sits on the south-west flank of Mulhacén, the highest peak in mainland Spain, where the Trevélez river meets a smaller stream, and its three barrios climb 190 metres from bottom to top — the highest house in the Barrio Alto reaches 1,610 metres. That altitude is the whole industry: the air is thin, cold and dry enough that ham can be cured here with nothing but salt and time, no smoke and no additives, over as much as two years. Jamón de Trevélez has a protected geographical indication and is the only ham indication in Spain defined by altitude. Alongside the ham the village runs on cherry tomatoes and around nine hundred head of livestock.

Trevélez: Ham Cured in Thin Air

Go through the eleven original cave dwellings kept at the Centro de Interpretación

See a zambra danced and work out how it differs from the flamenco performed everywhere else

Find out where the zambra came from — Morisco wedding ritual, not Andalusian cante

Walk up the Camino del Sacromonte for the view straight across the Darro at the Alhambra

Read Lorca's Romancero Gitano and work out which parts of it are this hillside

Sacromonte is on the eastern edge of Granada in the Valparaíso valley, directly across the Darro from the Alhambra — the traditional quarter of Granada's Roma, who lived in caves dug into the hillside. Lorca wrote them into the Romancero Gitano. The zambra danced here is its own form, distinct from the rest of flamenco, and descends from Morisco wedding ceremonies rather than from the Andalusian cante. The Centro de Interpretación del Sacromonte keeps eleven of the caves in their original state and opens them to the public.

Sacromonte: The Cave Quarter Facing the Alhambra

Walk through the Nasrid Palaces at your booked time, as far as the Court of the Lions

Climb the Torre de la Vela on the Alcazaba, built between 1238 and 1279, for the view over Granada and the Vega

Walk the gardens of the Generalife, the Nasrid kings' villa above the palaces

Go into the Palace of Charles V, begun in the 1520s inside the Nasrid walls

The Alhambra is the palace-city on its hill above Granada, built for the Nasrid emirs and their court and later lived in by the Kings of Castile; the decoration of the Nasrid Palaces is one of the high points of Andalusi art. It became Spain's first UNESCO World Heritage Site in 1984, together with the Generalife, the Nasrid kings' country villa and gardens just above it, and in 2016 it had over 2.6 million visitors, second in Spain only to the Sagrada Família. When Granada surrendered in 1492, the Catholic Monarchs' men raised the cross and their banner on the Tower of Comares, and in the 1520s Charles V began a Renaissance palace inside the walls. On the Alcazaba, the Torre de la Vela, built between 1238 and 1279, had a bell rung at dawn to tell the farmers of the Vega when to water.

The Alhambra: The Nasrid Palaces, the Alcazaba and the Generalife

Visit Mini Hollywood Oasys, one of the three western theme parks built on the sets of the Tabernas Desert, alongside Fort Bravo Texas Hollywood and Western Leone

Take a guided 4x4 tour into the Tabernas Desert, Europe's only desert, north of Almería with 15–22cm of rain a year

Look for Bonelli's eagles and ocellated lizards on a walk in the Tabernas badlands

Tabernas gets between 15 and 22 centimetres of rain a year, which makes it the only true desert in continental Europe. The rain that does fall is torrential, and because the marl and sandstone cannot hold it the water simply erodes the ground into badlands — which in the 1960s Italian directors worked out looked exactly like Mexico and Arizona and cost a fraction as much to film in. Hundreds of westerns were shot here. Three of the sets are still standing and running as western parks, and the badlands around them are a serious raptor site.

The Tabernas Desert: Western Film Sets in Europe's Only Desert

Walk between Pampaneira, Bubión and Capileira, the three villages of the Poqueira gorge on the south slope of the Sierra Nevada

Look at the flat-roofed houses of the Alpujarras, the North African mountain architecture that the Muslim inhabitants of Al-Andalus brought to these terraced hillsides

Buy a handwoven jarapa rug in Pampaneira, in the Alpujarran weaving tradition

Walk part of the GR 7 long-distance footpath that crosses the Alpujarras

The Alpujarras are the south slope of the Sierra Nevada, terraced and irrigated on a system the Muslims built and the villages still use, with flat-roofed houses of slate and clay that belong architecturally to North Africa rather than Spain. This is where the Moriscos were finally pushed after Granada fell, and where they rebelled in 1568. Pampaneira, Bubión and Capileira climb the Poqueira gorge one above another, and the walk between them is short, steep and the best introduction to the range.