Ride the road up from Covadonga to the Lagos de Covadonga, the twin lakes Enol and Ercina, one of the classic climbs of the Vuelta a España

Visit the Santa Cueva de Covadonga, the sanctuary cave that holds the tombs of the kings Pelagius and Alfonso I, from the 722 Battle of Covadonga that began the Reconquista

See the Basilica de Santa María la Real, the neo-Romanesque basilica built in 1886–1901 by Roberto Frassinelli

In 722 a small Visigothic force under Pelagius beat an Umayyad column in a valley below these mountains, and Spain has treated it ever since as the moment the Reconquista started — eight centuries of it, finishing at Granada in 1492. The sanctuary is built around the cave where it is said to have happened, with the tombs of Pelagius and Alfonso I inside it. The road up to the lakes above is one of the hardest finishes in the Vuelta a España: twelve kilometres with pitches over 15 per cent, ending at two glacial lakes at about 1,100 metres.

Covadonga: Pelayo's Cave and the Climb to the Lakes

Stand under the so-called Roman bridge and find out that it is medieval, and that everybody calls it Roman anyway

Work out what happened here: the capital of the kingdom of Asturias from 722 until 774, the only Christian state left in Iberia

Find the cross hanging beneath the central arch of the bridge — a copy of the Victory Cross, which began as the oak cross Pelayo carried at Covadonga

Go into the chapel of Santa Cruz, raised over a dolmen of the third millennium BC by King Favila and Queen Froiluba and consecrated on 27 October 737 to hold Pelayo's cross

Drink sidra poured properly — from arm's length, a couple of fingers at a time, drunk immediately

After the victory at Covadonga in 722 Pelayo made Cangas de Onís his capital, reusing the Roman settlement already there, and it stayed the capital of the kingdom of Asturias until 774 — which makes this small town on the Sella the first seat of the only Christian kingdom left in Iberia. The famous humpbacked bridge over the river is universally called the Roman bridge and is not: it was built in the Middle Ages. Pelayo's tomb is up the valley at Covadonga.

Cangas de Onís: The First Capital of Christian Spain

Walk the Ruta del Cares from Caín into the narrowest part of the gorge, along the path cut for the canal, and back

Stop at the Mirador del Tombo above the Cares, opened in 1964, and use its engraved panel to name the peaks

Find the Chorco de los lobos, the stone wolf trap near Caín that was used for centuries

Taste Valdeón, the blue cheese made at Posada de Valdeón

Caín is a hamlet of about seventy people at 460 metres in the Valdeón valley, at the León end of the Cares gorge. The path through the gorge to Poncebos, a little over 12 kilometres, began as the track for the channel feeding a small power station opened at Camarmeña-Poncebos in 1921, and was improved into a footpath between 1945 and 1950; about 300,000 people a year now walk it, and in places it runs along the cliff with an unprotected drop below. Caín's Gregorio Pérez, 'El Cainejo', made the first ascent of the Naranjo de Bulnes with Pedro Pidal on 5 August 1904.

Caín and the Cares Gorge: The Divine Gorge From the León Side

Walk up the old path from Poncebos, which is how the village was supplied for centuries

Take the funicular back down and work out what 402 metres of tunnel at 18.19% means

Work out what the funicular changed for fifty people, and what it may also have cost them

Walk up from Bulnes towards the Naranjo de Bulnes for the view of the face

Eat Cabrales in the village that is surrounded by the caves it is cured in

Bulnes has about fifty inhabitants and no road. For centuries the only way in was a steep path up from Poncebos, which is how everything the village used had to arrive. In the 1990s the Principality decided to end that isolation and bored a funicular through the Peña Maín: a tunnel climbing 402 metres at a gradient of 18.19%, opened in 2001, and by 2011 half a million people had used it. You can still walk the old path, and walking it is the point — it tells you what fifty people did every time they needed anything.

Bulnes: A Village Reached Through a Mountain

Take the cable car and work out that it gains 753 metres in 1,840 metres of cable

Walk from El Cable towards the Áliva refuge and down to Espinama, which is the classic day

Work out that the walk you have just skipped would have taken several hours

Look for chamois on the rock above the top station, which are used to people

Walk up from Fuente Dé on foot by the canal route instead, if you want to earn it

At the head of the Liébana the mountains simply stop being walkable and become a wall, and a cable car goes up it — 753 metres of vertical in 1,840 metres of cable, from the valley floor to a station called El Cable on the rim. It is the best-known tourist installation in Cantabria and it puts you, in four minutes, in high-mountain terrain that would otherwise be several hours of climbing. From the top you can walk to the Áliva refuge and down into Espinama, or go on into the central massif of the Picos.

Fuente Dé: Seven Hundred Metres Straight Up

Go into Tito Bustillo and find the main panel of horses and deer

Work out how it was found: young cavers in 1968, and who the cave is named after

Walk the seafront and find the indiano houses built with American money

Be at the bridge in August for the finish of the Descenso del Sella

Find the dinosaur footprints on the rocks along this coast, which are signposted from the town

A group of young cavers found the painted gallery at Tito Bustillo in 1968 and named it after one of their number who died on a later expedition. It holds Palaeolithic painting of the first rank — a main panel of horses and deer in red and black, and a separate chamber of vulval engravings — and it is part of the Altamira World Heritage listing. The town sits where the Sella reaches the sea, so it is also the finish of the Descenso del Sella every August, and it has a seafront of indiano mansions built with money from the Americas.

Ribadesella: A Cave, a River and a Race

Paddle the Arriondas to Ribadesella run yourself — the river is open all summer and outfitters rent everything

Come for the race on the first Saturday of August after the 2nd and watch the noon start — paddles locked in a frame that releases when the light goes green, after Dionisio de la Huerta's verses are read out

Ride the Tren Fluvial from Arriondas, which runs beside the river with stops to get out and watch

Find out how it started: a few friends going down the river for fun in 1929, fixed at this course in 1932

Finish at Ribadesella and work out how twenty kilometres of river feels from inside a boat

In 1929 Dionisio de la Huerta and a few friends paddled down the Sella for the fun of it. They repeated it in 1930 and 1931, fixed the start and finish at Arriondas and Ribadesella in 1932, and turned it into a race with thirteen paddlers. It now runs twenty kilometres down the river on the first Saturday of August following the 2nd, has been a Festival of International Tourist Interest since 1980, and finishes under the bridge at Ribadesella. Renfe runs a Tren Fluvial down the valley beside the race so the crowd can follow the boats.

Descenso del Sella: Twenty Kilometres of Canoes

Tour the castle and its museum on the life of Francis Xavier

Find the dance of death painted on the walls of the Torre del Santo Cristo, the only one of its kind in Spain

Walk through the Foz de Lumbier, the Irati's gorge, and watch the vultures on its walls

Francis Xavier was born in this castle in 1506 and took his name from it, and went on to carry Christianity to India and Japan. The castle goes back to the 10th century; in 1516 Cardinal Cisneros ordered it pulled down because its lords had fought for Navarre's independence, and his men razed the outer wall and filled the moat but left the core standing. In the Torre del Santo Cristo are a late-Gothic crucifix and wall paintings of the dance of death, the only ones of their kind in Spain. Eight kilometres west, the Irati has cut the Foz de Lumbier, a gorge just over a kilometre long between walls 150 to 400 metres high where griffon and Egyptian vultures nest.

Javier: Francis Xavier's Castle and the Foz de Lumbier

Find Jeff Koons' 12m-tall floral sculpture "Puppy" — replanted twice a year with 60,000 flowering plants — guarding the Guggenheim's entrance

Inside, find Richard Serra's "The Matter of Time" in Gallery 104 — eight weathering-steel sculptures filling a room 130m long

Walk from the Guggenheim to the Bilbao Fine Arts Museum through Doña Casilda Iturrizar Park, and compare the two museums' opposite approaches to art

Cross the Zubizuri footbridge and find Calatrava's glass-brick deck, now covered with a non-slip mat after years of complaints it was dangerous when wet

Bilbao was a dying port city with a poisoned river in 1991 when it gambled public money on a Frank Gehry building nobody could picture. It opened in 1997, drew a million visitors in its first year, and gave planners everywhere a phrase — the Bilbao effect — for the belief that one spectacular building can turn a city round. Most attempts since have failed. What is often missed is that Bilbao also cleaned the Nervión, built a metro and moved the port, and the Fine Arts Museum five minutes away had a better collection all along.