And still the sparkling examples of modern architecture keep coming. Newish riverside attractions include the Maritime Museum, the Euskalduna concert hall and a sleek tramline. Add to this a swish new airport, again by Norman Foster, and you have a model for urban redevelopment that most city fathers across Europe can only dream about.

The river doesn’t just serve as a backdrop for Bilbao’s new tourist attractions, it also divides old and new. To its east the narrow streets of the Casco Viejo, or old city, are the most atmospheric, especially the Siete Calles (‘Seven Streets’) district, thick with bars and restaurants, and surrounded by monuments such as the Gothic Catedral de Santiago, the vast Mercado de la Ribera food market and San Antón church. Walking tours of the Casco Viejo take place at 10am on Thursdays, Fridays and Saturdays, leaving from the tourist office (see below) opposite the Teatro Arriaga (€3, 90mins).

Along and beyond the river’s west bank, the city’s new architecture is a perfect counterpoint to the classic Spanish forms of the old city. For a bird’s-eye view, take the funicular (every 15mins) from the plaza of the same name up to Artxanda, which overlooks the city. From here, the titanium waves of the Guggenheim building (Avenida Abandoibarra 2, 944 359 080, www.guggenheim-bilbao.es, closed Mon), set against the river and green hills beyond, look incredible. Also along this stretch of river is the high-spec Palacio de Congresos y de la Música Eukalduna concert hall (Avenida Abandoibarra 4, 944 035 000, www.euskalduna.net) and, further along, the Maritime Museum Ría de Bilbao (Muelle Ramón de la Sota 1, 902 131 000, www.museomaritimobilbao.org).

Inside the ‘Goog’, its three floors, bathed in natural light, are a handful of Picasso sketches from Paris, a collection of pop art, much by Anselm Kiefer, plus temporary shows on rotation from the foundation’s other branches. Gehry’s breathtaking design overshadows a somewhat disappointing collection, guarded on each side by Jeff Koons’s vast, flower-carpeted Puppy and Louise Bourgeois’ twisted spider, Maman. It also overshadows the nearby Museo de Bellas Artes (Plaza del Museo 2, 944 396 060, www.museobilbao.com, closed Mon), whose mainly Spanish and Basque collection ranges from Romanesque to the present day.

From the Bellas Artes, it’s a short walk to the central shopping hub of Plaza Moyúa, and from there the spinal Gran Vía, lined with grand 19th-century edifices, leads towards Arenal bridge and the Casco Viejo.

• Tourist information: Plaza Ensanche 11 (944 795 760, www.bilbao.net).