Coimbra or Madrid?

Neither city is built for swimming, but Coimbra at least has the sea within an hour. Figueira da Foz has a very wide sandy beach, with Buarcos at its end and quieter stretches at Quiaios further up. The water is cool and often windy, and gentler river beaches lie on the Mondego in the hills.

Madrid has nothing like this. The coast is too far for a day trip, and summer swimming means the municipal open-air pools or the reservoirs below the Guadarrama.

Coimbra's cooking is hearty and regional, and it is best as a single dedicated outing: suckling pig with Bairrada sparkling wine at the roadside restaurants of Mealhada, or chanfana from the eastern hills. In town, eating out mostly means simple tascas and convent pastries, and the choice soon runs thin.

Madrid offers far more. Eating there is a whole evening's habit, from the zinc counters of La Latina and Lavapiés to cocido, churros at small hours, Galician seafood and Basque grills, and a top tier of tasting menus. The market halls of San Miguel and Antón Martín add plenty more choice.

Coimbra's heritage is older and compact: the UNESCO-listed university with the gilded Biblioteca Joanina, the Romanesque Sé Velha, the royal tombs at Santa Cruz and the half-buried Santa Clara-a-Velha. You can see it all in a day or two, and it gives a medieval depth that central Madrid lacks.

Madrid outweighs it on the strength of painting. The Prado, Reina Sofía and Thyssen along one avenue can fill several days, and the Royal Palace, Plaza Mayor and the Goya frescoes of San Antonio de la Florida add a grand, later layer.

Coimbra's nights follow the student year. The bars around Praça da República and the upper town fill late during term, and the Queima das Fitas takes over the streets in May. In July and August most evenings end with dinner by the river.

Madrid is a different scale altogether. Clubs don't start before two, and each district has its own crowd: rock bars in Malasaña, the gay scene in Chueca, terraces in La Latina, techno near Gran Vía. Plazas stay busy well after midnight in every season.

The two are broadly level for the outdoors, but the landscapes are very different. Coimbra's surroundings are green and wooded, with the ancient trees of the Buçaco forest half an hour away, slate villages and chestnut woods in the Serra da Lousã, and kayaking down the Mondego valley.

Madrid's outdoors is higher and bare granite. The Sierra de Guadarrama, an hour north, has the boulders of La Pedriza, glacial lakes below Peñalara and some winter skiing. In town, Retiro and Casa de Campo are larger green spaces than anything in Coimbra, though the plains around the city are just farmland.

Both make excellent bases, though Madrid has the edge. From Coimbra, Porto and the canal town of Aveiro are easy by train, and the Roman mosaics of Conímbriga are close by. The great monasteries of Batalha, Alcobaça and Tomar mostly need a car or coach.

Madrid's high-speed network puts more first-rate cities closer. Toledo and Segovia are each about half an hour away, and Ávila, Salamanca and Cuenca are not much further. El Escorial and Aranjuez are closer still.

Coimbra has two good child-sized outings, the miniature houses of Portugal dos Pequenitos and the Exploratório science centre. But the climb to the old town on cobbles and stairways is hard work with a pushchair.

Madrid gives families more to do and an easier time getting about. There are rowing boats and puppet shows in the Retiro, a zoo, cable car and funfair at Casa de Campo, theme parks further out and a flat centre. The trade-offs are the summer heat and very late meal times.

Coimbra is small enough to walk, but almost every visit involves the steep haul from the Baixa up to the university, softened somewhat by a public lift and a funicular. Buses cover the river crossing, and a car helps for the forests and monasteries outside town.

Madrid is easier in every way. Its centre is flat from the Royal Palace to the Prado, and the large air-conditioned metro runs straight to the airport. Atocha and Chamartín stations link directly into the fast trains.

Shopping in Coimbra is a short stroll down Rua Ferreira Borges plus a few things to take home: hand-painted faience, convent sweets and Bairrada wine.

Madrid is a proper shopping city. It has luxury houses along Calle Serrano, department stores and flagships around Gran Vía and Sol, independent and vintage shops in Malasaña and Conde Duque, and the Sunday Rastro flea market below La Latina.

Coimbra makes a budget go further on almost every count. Most of the sights are a short walk apart and the city buses are cheap, so getting about costs very little. The time to watch is May and the graduation weeks, when the Queima das Fitas fills the rooms and prices go up.

Madrid is a mid-priced capital rather than a bargain. Its metro is inexpensive, and the Prado and the other great museums have free entry at set times, so its best sights can cost less to see than Coimbra's library and palace rooms. Eating out stays fairly modest thanks to the midday set menu and tapas with a drink. Hotels get dearer around big events, though, and over a whole stay Madrid costs more.

Coimbra has one thing Madrid cannot offer, its own fado. It is sung by men in black academic capes to the Coimbra guitar, both in small old-town houses and on the steps of the Sé Velha. Beyond fado there is the Teatro Académico de Gil Vicente and touring shows at the São Francisco arts centre.

Madrid's stage life is far broader. It has opera at the Teatro Real, the national orchestra at the Auditorio Nacional, zarzuela, Gran Vía musicals, serious flamenco tablaos and long-standing jazz clubs.

Coimbra is the better place to unwind. The thermal spas of Luso and Curia, with Curia's lake and Belle Époque hotels, are about half an hour north, and the city itself is quiet outside term.

Madrid offers a few Arab-style bathhouses under brick vaults and hotel spas. Its late, noisy rhythm means rest comes mostly from a lazy afternoon in the Retiro.