Eat the vegetables — artichokes, borage, cardoon, asparagus, piquillo peppers — which is what the town is for

Come in April for the vegetable fair, which is a serious event here rather than a novelty

Find out who Quintilian and Prudentius were, and that both came from this town

Find out what the Fames Calagurritana was and find the Matrona on the town's arms

Go into the cathedral, which stands outside the old walls rather than inside them

Built on the Vasconic settlement of Kalakorikos, this was Roman Calagurris Nassica Iulia. It became famous for Pompey's siege, in which almost the whole population is recorded as having starved rather than surrender — the Fames Calagurritana, still symbolised on the town's arms by the Matrona. It produced Quintilian, the great teacher of rhetoric, and Prudentius, among the finest Christian poets of antiquity, whose Peristephanon includes hymns to Calahorra's own patrons Emeterius and Celedonius. It is now the vegetable capital of the Ebro, with a cathedral and a vegetable fair in April that the town takes very seriously indeed.

Calahorra: A Roman Town That Ate Itself

Get into the free thermal pools at the riverside, where hot spring water meets the Cidacos

Take the waters properly at the spa if you want them at full temperature

Watch the griffon vultures on the cliffs above the village, which is a substantial colony

Walk the greenway along the old Cidacos railway line up the valley

Go on up the valley to the dinosaur track sites towards Enciso

Arnedillo sits in the Cidacos gorge in the Rioja Baja, with hot springs that surface in the riverbed itself — there are free public pools at the water's edge where the thermal water mixes with the river, and a paying spa in the village for the same water at full temperature. The cliffs above hold a large griffon vulture colony, close enough to the road to watch from below. The Cidacos valley is also dinosaur track country, with several signposted sites on the way up towards Enciso.

Arnedillo: Hot Water and Vultures

Take the waters at the Baños de Fitero, in use since the Roman settlement of Tudején

Go into Santa María la Real, founded in 1140 on a donation from Alfonso VII by monks from Escaladieu

Find out what Raymond of Fitero raised at Calatrava, and that he never got this monastery back

Work out what the name means and which two kingdoms and two dioceses met here

Find the older bath structure underneath the 19th-century spa buildings

The name Fitero means frontier, because in the 12th century the monastery here sat on the line between Castile and Navarre and between the dioceses of Calahorra and Tarazona. Saint Raymond of Fitero founded the monastery with Cistercians from the abbey of Escaladieu in the high Pyrenees, on a donation from Alfonso VII in 1140. He then raised a Cistercian militia, took it to Calatrava, and out of it came the Military Order of Calatrava. He never got his own monastery back: his monks were beaten and driven to Calahorra, a second Cistercian community arrived in 1161 under a new abbot, and Raymond died in exile at Ciruelos. Downstream on the Alhama are the baths, in use since Roman Tudején, now a working spa on hot mineral water with a Moorish bath structure underneath the 19th-century buildings.

Fitero: Monastery, Frontier, Baths

Walk the Virgen del Campo site and count tracks — around five hundred of them in one slab

Work out which prints are carnivores and which are two-legged herbivores, and how you can tell

Work out how they survived: a waterlogged early Cretaceous plain, buried, hardened, then uncovered again by erosion

Go to the palaeontological centre in the village to find out which species left them

Follow the marked route to the other sites around Enciso — there are over three thousand prints in this one municipality

In the early Cretaceous this part of La Rioja was a waterlogged plain, and animals walking across the mud left prints that were buried, hardened and then exposed again as erosion stripped the layers above. There are over three thousand dinosaur footprints in the municipality of Enciso alone. The Virgen del Campo site, on the right bank of the river a few metres from the bridge, has around five hundred tracks of both carnivores and herbivores walking on two legs, and is one of the most complete anywhere.

Enciso: Three Thousand Dinosaur Footprints

Walk the towers and the wall walks and work out how much of the silhouette is decoration rather than defence

Find the black mulberry inside, which is protected as a natural monument of Navarre

Work out what was lost in 1813, when Espoz y Mina had the palace burnt to deny it to the French

Find out what Charles III put in here that a castle would never have had — gardens, a menagerie, hanging gardens

Come in summer for the Festival de Teatro Clásico, which uses the palace as its main venue

Charles III of Navarre turned an existing castle at Olite into a permanent royal seat in the 15th century and gave it everything a court of the period was supposed to have: towers, gardens, moats, hanging gardens, even a menagerie. The silhouette of towers above the walls is why it is probably the most emblematic civil building in Navarre and its most visited monument. In 1813 the guerrilla leader Espoz y Mina had it burnt, to stop Napoleon's troops fortifying it — so the towers survive and the interior decoration and the gardens are gone for good.

Olite: The Palace the Kings of Navarre Built for Themselves

Drive or cycle the tracks through the Bardena Blanca, the central and most desert part of the whole area

Find Castildetierra, the isolated eroded spire that is the single most photographed thing here

Work out the geology: sediment dumped into a closed inland sea as the Pyrenees rose, then drained and eroded ever since

Go up to a mirador on the edge of the plateau and see the whole thing laid out below

Check what the military firing range is doing before you plan a route — part of the Bardenas is still one

The Bardenas are badlands in southern Navarre — clay, gypsum and sandstone with almost no vegetation, eroded by water and wind into ravines, flats and isolated cabezos, and traditionally divided into three: El Plano, the Bardena Blanca and the Bardena Negra. The ground is Tertiary and Quaternary material dumped into the Ebro basin when the Pyrenees and the Iberian range rose and closed it off into an inland sea; the sea drained, and the erosion that started then is still going. It was made a UNESCO Biosphere Reserve on 6 November 2000. It looks like nowhere else in Europe and is used constantly as a film location for exactly that reason.

Bardenas Reales: The Desert in Navarre

Go into the cloister and work out why the mosque underneath had to be demolished rather than adapted — the two buildings faced different ways

Find the Puerta del Juicio on the west front and read the relief of the damned

Find out who Benjamin of Tudela was and how far he travelled in the 12th century

Eat the vegetables — this is the Ribera, and the artichokes, borage and asparagus are the point of the place

Come in spring for the vegetable season, which is short and taken very seriously here

Tudela was a major Muslim town on the Ebro, and its cathedral — late Romanesque on Cistercian lines, begun at the end of the 12th century under Sancho VI and finished under two successors — was built on the site of the Great Mosque of the 9th to 11th centuries. Because the two buildings did not face the same way the mosque had to come down, and only some of its foundations were reused. The Judgement Doorway on the west front carries a crowded relief of the damned. Benjamin of Tudela, the 12th-century Jewish traveller whose account of a journey across the Mediterranean and the Near East is a major medieval source, was born here. The town is also the vegetable capital of the Ebro.

Tudela: Mudéjar on the Ebro

Be in the village for a procession and understand before you go what you are actually going to see

Find out why this survived here when public flagellation was suppressed everywhere else in Spain

Work out what a disciplinante has to be to take part: adult, male, and vouched for by a priest

Climb to the castle and the fortified church on the rock above the Ebro

Work out what the Cofradía de la Santa Vera Cruz is and that it has organised this from the start

At Easter and on a few other days, men in white robes with hoods walk in procession through San Vicente de la Sonsierra scourging their own backs with a rope discipline, and are then pricked to draw the bruising off. It is the only place in Spain where the penance is still practised, it has always been run by the Cofradía de la Santa Vera Cruz, and it was recognised as of National Tourist Interest in 2005. Disciplinantes must be adult, male, and vouched for by a priest as a Christian acting in good faith. The village sits on a rock above the Ebro with a castle and a fortified church.

San Vicente de la Sonsierra: The Picaos

Be on the Cuesta de los Danzadores for the descent and work out that they are spinning the whole way down

Look at the stilts and the yellow skirts and work out how the costume is meant to work with the spin

Come in July for the Magdalena or in September for the Gracias, which are the two occasions

Walk up to the Ermita de la Magdalena and find the intermittent spring beside it

Work out why this is called the oldest folk tradition in La Rioja

Anguiano's stilt dancers are said to be the oldest folk tradition in La Rioja. Eight men in yellow skirts, on stilts about half a metre high, spin down the Cuesta de los Danzadores — a steep cobbled street running from the church to the Plaza Mayor — rotating the whole way, held up only by momentum, with the crowd packed on both sides. They do it for the Magdalena in July and again at the Gracias in September. It looks impossible and people do get hurt.