You could visit the Guggenheim Museum; stroll around the old town (Casco Viejo) - full of interesting shops and great little places to eat or drink. Go tapas-hopping! (in the Basque Country, tapas are called pintxos ("pinchos"). You can eat standing up at the bar or at a table. Take a visit to the city's traditional La Ribera market (from early morning until around 2pm, except Sundays when closed) or take the funicular up to Mt. Artxanda for views over Bilbao. Visit the UNESCO World Heritage Transporter "Vizcaya Bridge" at Getxo, down at the mouth of the estuary (ask hotel staff for directions) - you can ride in the gondola across in one direction and walk back in the other.