There are two wonderful museums to visit and explore art in Bilbao:
Guggenheim Bilbao, Abandoibarra Et.2: Having seen the Guggenheim branches in New York, Berlin and Venice and knowing about the impact that the Frank Gehry building has on Bilbao from a lecture that I heard Gehry give in Santa Fe NM, this has been high on my list to see. The building and setting are spectacular. The building is constructed of iron, stone and glass with a titanium plate covering that has been curved into some incredible curved shapes. You can’t miss the huge floral dog by Jeff Koons at the entrance.
There are great works by Mark Rothko, Jorge Oterza, Willem de Kooning, Cy Twombly, Robert Rauschenberg, Clyfford Still, Andy Warhol, Antoni Tapies, Anselm Kiefer, Jim Dine and Sol LeWitt. They also have temporary exhibitions to view.
Bilbao Fine Arts Museum: I did not know what to expect but it turns out this is definitely one of the most important art museums in Spain and is not to be missed! I was greatly impressed with its contemporary abstract art, its sculptures, and its other collections. You will see works by Antoni Tapies, Mary Cassatt, Miguel Barcelo, Goya, El Greco, Paul Gaugin and Eduardo Chillida to name a few. The building is really great, particularly the new modern wing. There is a small cafe to take a break. I saw two great temporary expositions also so make sure to check the calendar before you go.