Walk the Greek Neapolis and then the Roman town and work out where one ends and the other begins

Find the Palaiapolis at San Martí d'Empúries — the original island colony, now a village on a low rise

Work out what happened here in 218 BC and why it mattered to the whole peninsula

Find the mosaics and the Asklepios statue, and then find out which one on site is a copy

Stand on the beach the Romans landed on and work out why they chose an existing Greek port

In 575 BC the last wave of Greek colonisation reached the peninsula — Phocaeans out of Massalia, trading at long range — and they put their first settlement on an island off this coast, the Palaiapolis, which is now San Martí d'Empúries and is still inhabited. The Neapolis, the new town, grew on the mainland south of it, trading with the Indiketa people already there. The Romans landed here in 218 BC at the start of the Second Punic War and eventually built their own city beside the Greek one. It is the only site in Iberia where a Greek and a Roman town sit side by side.

Empúries: Where Greece Landed in Iberia

Walk the lanes of Peratallada round its castle

Climb up through the Gothic quarter of Pals to the Torre de les Hores

Buy Arròs de Pals, the rice grown in the fields below the village

Go to Peratallada's medieval market on the first weekend of October

Inland from the Costa Brava two medieval villages stand seven kilometres apart. Peratallada, first recorded for its 10th-century castle, was declared a historic-artistic ensemble as one of the most important and best preserved medieval centres in Spain, and holds a medieval market on the first weekend of October. Pals has a Gothic quarter of cobbled streets, pointed windows and stone balconies round the Romanesque Torre de les Hores, built between the 11th and 13th centuries, and the rice fields below it grow Arròs de Pals.

Pals and Peratallada: The Medieval Villages of the Empordà

Work out what the building is: the theatre he knew as a child, burned in the Civil War, and rebuilt by Dalí as one continuous work

Find the Mae West room, an anamorphic living-room installation that only resolves into a face from one exact spot

Find the Cadillac plujós, the full-size car installation based on his Rainy Taxi of 1938

Go down to the crypt below the stage, where Dalí is buried in the middle of his own museum

Stand under the glass geodesic dome over the old stage and work out that every decision in the building was his

Salvador Dalí was born in Figueres on 11 May 1904, in a first-floor flat on Carrer Monturiol. The heart of his museum is the town theatre he knew as a child, burned during the Civil War and left a ruin for decades until he rebuilt it as a single enormous work of his own — designing the rooms himself and crowning the old stage with a glass geodesic dome. It opened on 28 September 1974 and kept growing into the mid-1980s. He lived in it from 1984 until his death in 1989 and is buried in a crypt below the stage floor.

Figueres: The Museum Dalí Built for Himself

Climb to Begur castle and find the watchtowers built against the pirates

Walk the streets of the indianos' houses in Begur

Hear the habaneras at the Port Bo in Calella de Palafrugell

Walk the garden at Cap Roig above the sea

Begur grew rich on the indianos — local men who crossed the Atlantic, above all to Cuba, made their fortunes and came home to build — and five watchtowers against Moorish pirates stand round its castle. Below it are some of the best-known coves of the Costa Brava: Sa Riera, Aiguafreda, Sa Tuna, Fornells and Aiguablava, where a parador was built on the cliff in 1966. A few kilometres south, Calella de Palafrugell has kept the feel of a fishing village; on the first Saturday of July it holds the Cantada d'havaneres, the songs popular in Catalonia's fishing villages, in the Port Bo, and above it on Cap Roig are the botanical garden and the summer festival.

Begur and Calella: The Indianos, the Coves and the Habaneras

Climb to the monastery and look back down over the bay of Roses and the Cap de Creus

Work out why a church this size is on a remote headland at all — the answer involves relics shipped out of Rome in 610

Walk up to the ruined castle of Sant Salvador de Verdera above it, which is what protected the monastery

Work out why it was built here rather than in the valley, and what it was watching

Find out what happened after 1793, when the Benedictines left, and what the excavations after 1990 turned up in the lower cloister

Sant Pere de Rodes stands high on the northern flank of the Serra de Rodes, above El Port de la Selva, with the whole bay of Roses and the Cap de Creus laid out beneath it. It was repeatedly plundered from the 17th century and the Benedictines finally left in 1793. Excavations after 1990 turned up gold and silver coins, old ceramic tiles and Romanesque painting in a lower cloister nobody knew existed until the middle of the 20th century — and the scale of the church, absurd for so isolated a spot, is explained by relics identified as St Peter's, taken out of Rome by sea in 610.

Sant Pere de Rodes: A Monastery on the Cap de Creus Ridge

Go out to the end of the cape, the easternmost point of mainland Spain and of the Iberian peninsula

Look at the twisted rock, then at reproductions of The Persistence of Memory and The Great Masturbator, both of which are this peninsula

Go into Dalí's house at Port Lligat, the bay next to the village, where he lived and worked for most of his life

Find the Café Melitón, where Marcel Duchamp played chess — he rated the local fishermen as serious opponents

Work out why the artists came here: one difficult road in, and a village that stayed a fishing village long after the rest of the coast stopped being one

Cadaqués sits on a bay in the middle of the Cap de Creus peninsula with one bad road in, which is why it stayed a fishing village long enough to collect Picasso in the summer of 1910, then Miró, Duchamp and a good many others. Dalí spent a childhood summer here in 1916 with the Pichot family that he later said made his career, and kept a house at Port Lligat next door. Beyond the village the cape is 190 square kilometres of natural park, wind-scoured and almost treeless — and the easternmost point of Catalonia and so of mainland Spain and the Iberian peninsula.

Cadaqués and Cap de Creus

Walk the Call, one of the best-preserved medieval Jewish quarters in Spain, and find out who Nahmanides was

Climb the cathedral steps and stand under the widest Gothic nave in the world — 22.98 metres, beaten by no church but St Peter's

Walk the Passeig de la Muralla along the top of the Carolingian and late-medieval walls, with its viewpoint over the whole city

Find the confluence: Girona sits where the Ter, Onyar, Galligants and Güell all meet

Photograph the coloured houses hanging over the Onyar, which is the standard view of the city for a reason

A Jewish community is documented in Girona from about 885, and by the 12th century the town held one of the most important Kabbalistic schools in Europe; its rabbi, Moshe ben Nahman — Nahmanides — was made Great Rabbi of Catalonia. It ended in 1492 with the Alhambra Decree. The Call is one of the best-preserved Jewish quarters in Spain. The cathedral above it has the widest Gothic nave in the world at 22.98 metres, second-widest of any church after St Peter's, redesigned by Pere Sacoma in 1312 with a vault 35 metres up.

Girona: The Call and the Widest Gothic Nave on Earth

Stand in front of the 12th-century portal and work out that it is laid out as a Roman triumphal arch

Read the carving as a programme rather than decoration, and work out what it is narrating

Find the tombs of the counts of Barcelona and Besalú

Find out what the scriptorium here produced and why Ripoll is named beside Fleury and Montecassino

Go on to Sant Joan de les Abadesses, which Wilfred founded for his daughter Emma

Wilfred the Hairy reconquered and repopulated the Ripoll valley and the Vic plain between 878 and 881 and founded this monastery around 880, probably on a Visigothic site. It became the burial place of the counts of Barcelona and of Besalú, and its scriptorium made it one of the great cultural centres of medieval Europe, in the same conversation as Saint-Denis, Fleury and Montecassino. In the 12th century it got a new doorway built as a triumphal arch — a vast carved programme that is one of the major works of Catalan Romanesque sculpture.

Ripoll: The Cradle of Catalonia

Stand on the balcony of the Plaza del Cabildo and look straight down the cliff at the Guadalete

Work out what de la Frontera means, and what happened to the 1253 treaty that let the Moors stay

Find out that this was its own taifa from 1012 under a Berber ruler until Seville absorbed it in 1069

Walk the old town lanes, which are narrow enough that buses have to fold their mirrors in

Go into Santa María and San Pedro, the two churches that compete for the skyline

Arcos sits on a sandstone spur above a loop of the Guadalete with a sheer drop on one side, and it is the gateway to the route of the pueblos blancos. After the caliphate of Córdoba collapsed, the taifa of Arcos was proclaimed in 1012 under Ben Jazrum, a Berber; al-Mutadid of Seville swallowed it in 1069. Castile took it by treaty in 1253 on terms allowing any Moor who wished to stay — terms Alfonso X did not keep — and he retook it outright in October 1264 during the Mudéjar revolt. The Plaza del Cabildo at the top has the castle, the church of Santa María, the parador and a balcony straight over the drop.