Go into the Sancti Spiritus university building, founded by papal bull in 1540 and closed in 1842

Work out what five faculties in a Gipuzkoan town of this size actually meant

Find out what conditions the town attached to joining Gipuzkoa in 1540

Go into the Arrikrutz cave under the town

Drive up the valley to Arantzazu, which is the other half of a day here

In 1540 Bishop Rodrigo Mercado de Zuazola founded the University of Sancti Spiritus at Oñati by bull of Paul III — the first university in the Basque Country, with faculties of law, canons, arts, medicine and theology, running until it closed in 1842. The town negotiated its own annexation to Gipuzkoa in 1540 on conditions including a road and an increased endowment for the university. It was a Carlist stronghold in the 19th century and the Pretender's headquarters. The Arrikrutz cave beneath it is open, and Arantzazu is up the valley.

Oñati: The First University in the Basque Country

Stand in front of Oteiza's facade and count the apostles — there are fourteen, which is two too many

Work out why the frieze is at road level: the facade starts below the path you arrive on

Find Chillida's doors and then Lucio Muñoz's apse inside

Go down into the crypt for Basterretxea's wall paintings

Work out what it means that a religious building of 1950 was given to the artists it was given to

In April 1950 the Franciscan provincial proposed a new basilica at Arantzazu, high in the Gipuzkoan mountains, and the job went to the architects Sáenz de Oíza and Luis Laorga. What is remarkable is who else worked on it: Jorge Oteiza carved the main facade, with a frieze of fourteen apostles set at road level because the front starts below the path; Eduardo Chillida made the main doors; Lucio Muñoz painted the apse; Néstor Basterretxea did the crypt walls and Xabier Egaña the murals. It is effectively the Basque avant-garde of the 20th century working on one building.

Arantzazu: A Basilica Built by the Basque Avant-Garde

Tour the Idiazabal Cheese Interpretation Centre and taste raw-milk Latxa sheep cheese, D.O. since 1987

Find the reconstructed shepherd's txabola hut inside the museum

Drive the short pastoral route to the Ecomuseum of Pastoreo in Telleriarte

Buy a wheel of naturally smoked Idiazabal directly from a producer along the route

Idiazabal has been a protected designation since 1 October 1987, and the rules are strict: raw, unpasteurised sheep's milk only, and only from the latxa and carranzana breeds. It takes around seven litres of that milk to make a kilo of properly matured cheese. About five hundred farms and more than a hundred dairies work under the appellation, most of them making the cheese from their own flock alone. The smoked version, which is what most people picture, started as a by-product of curing cheese in shepherds' huts with a fire in them. In 1995 it took first prize at Parma as the best European sheep's cheese.

Idiazabal: The Shepherd's Cheese Route

Ride or walk a vía verde end to end and notice that the gradient never really changes

Work out why: the route is a railway grade, and a steam locomotive could not pull anything steeper

Go through the tunnels and over the viaducts, which are the original railway structures

Find the old station buildings on the route and see what they have been turned into

Work out which line this was, when it closed, and what it was carrying

Spain closed a great many branch lines and mining railways in the 20th century, and rather than let the trackbeds go the country turned them into the Vías Verdes — surfaced, waymarked routes for walking, cycling and riding, on grades no steeper than a steam locomotive could pull. That constraint is the point: they are almost flat, they go through the tunnels and over the viaducts the engineers built, and they make otherwise serious terrain accessible to anyone. The Ferrocarriles Vascongados route runs 13.6 kilometres between Soraluze-Placencia de las Armas and Anzuola.

Vías Verdes: Riding Spain's Abandoned Railways

Go into the Santa Casa, the original tower house, still standing inside the Baroque sanctuary built round it

Find the room where Ignatius convalesced and work out what was and was not available to read in it

Work out what happened at Pamplona in 1521 and how a broken leg redirected a religious order

Walk the Baroque basilica outside and compare its scale with the house at its centre

Work out why the Jesuits enclosed the house rather than replacing it

Íñigo López de Loyola was a soldier until a cannonball smashed his leg at Pamplona in 1521. Convalescing in his family's tower house at Azpeitia with nothing to read but a life of Christ and a book of saints, he changed direction entirely and became Ignatius of Loyola, founder of the Jesuits. In the 17th century the family house was enclosed inside a vast Baroque sanctuary, so that the original stone tower still stands intact in the middle of the newer building — the room where he read is still there.

Loyola: Where Ignatius Was Converted

Get to a village festival where aizkolaris are cutting and time a round yourself

Watch a harrijasotzaile lift and work out that the count, not the single lift, is the contest

Find out what palanka is and that the bar started out as a mining tool

Work out the role of the bet — these are not exhibitions, money is on them and always has been

See a pelota match in a village fronton afterwards, which is the other half of Basque sport

Herri kirolak are farm and quarry jobs turned into contests, and what holds the whole thing together is the bet. Aizkolaris chop through stacked logs against the clock. Harrijasotzaileak lift cylindrical and cubic stones of enormous weight, repeatedly. Teams pull on a rope in sokatira. The iron bar thrown in palanka started life as a mining tool, and in the old days the bets were settled in a meadow outside the village with no standardised weight — only the requirement that everyone in that particular wager used the same one.

Basque Rural Sports: Competitive Work

Cycle or walk the full Anillo Verde circuit round the edge of the city

Go to the Salburua wetlands, one of the most important breeding sites for waterbirds in the Basque Country, with around two hundred species recorded

Come in autumn for the deer rut at Salburua — the animals were introduced in the late 1990s and the berrea now happens inside the city boundary

Walk the medieval almond — the old town's concentric streets running round the hill

Work out what forty-two square metres of green space per inhabitant means when you are standing in the middle of it

Vitoria-Gasteiz was the European Green Capital in 2012, and the reason is the Anillo Verde — a ring of restored parks and wetlands right round the edge of the city, made mostly out of degraded ground: old gravel pits, drained marsh, industrial land. Counting it, Vitoria has about forty-two square metres of green space per inhabitant, among the highest in Europe. Salburua inside the ring is one of the most important sites in the Basque Country for breeding waterbirds, with around two hundred species, plus European mink and red deer introduced in the late 1990s whose autumn rut now draws people out of the city. Inside the ring is a medieval almond-shaped old town built in concentric streets on a hill.

Vitoria-Gasteiz: The Green Ring

Stand back and work out what the three colours of the titanium are meant to represent

Go down into the original cellars of 1858 and find the oldest bottles in the collection

Walk up into Elciego village and look back at the building from the church

Decide for yourself whether it belongs here, which is an argument people in the Rioja Alavesa actually have

Taste the wine, which is the reason any of this exists

Guillermo Hurtado founded Marqués de Riscal at Elciego in 1858 — the oldest winery in Álava — after importing nine thousand French vine cuttings to experiment alongside the Tempranillo and Graciano already here. In 2006 the estate became the Ciudad del Vino, and the building everyone comes for is Frank Gehry's, sandstone under a titanium roof: pink for red wine, gold for the netting on a Riscal bottle, silver for the capsule. It holds a hotel and two restaurants and sits in the middle of the vineyards below the village of Elciego, which has nothing else remotely like it. Whether it belongs there is a live argument in the Rioja Alavesa.

Elciego: Gehry in the Vines

Stand between the puente viejo and Calatrava's footbridge and work out how many centuries are in view

Find out what Alfonso XI granted the town in 1335 and what the bridge had to do with it

Walk the old quarter stacked up the hill above the port

Watch the fleet unload — this is one of the main fishing ports on the Cantabrian coast

Walk round to Arrigorri beach at the mouth of the ría

Alfonso XI granted Ondarroa the rights to the traffic over the wooden bridge across the Artibai in 1335, and the stone bridge that replaced it in the 18th century — the puente viejo — is still standing. Beside it Santiago Calatrava built a white asymmetric footbridge in the 1990s, so a working Basque fishing town has a 14th-century charter, an 18th-century bridge and a piece of late-20th-century engineering all within a hundred metres. The port is among the most important on the Cantabrian coast and the old quarter is packed onto the slope above it.