Just past the Carlton Hotel, turn left at Alameda Recalde. At the intersection with Licenciado Pozas, you'll see, on the left, the impressive Ledo Building, the headquarters of Basque health care system, by the Catalan architect Juan Coll-Barreu.
Keep going until Plaza Arriquibar, which leads to the entrance to the spectacular Alhóndiga Building. This former wine warehouse was left abandoned for decades until, at the beginning of the present century, designer Phillipe Starck undertook its renovation, converting it into a leisure and cultural centre. Both its modern exterior and interior are worth seeing. On the first floor you'll find Mediateka, a sort of library with newspapers, books and comics where you can rest your feet. If time permits, definitely go up to La Terraza (on the third floor; the elevator is located at the stairs to the right of the restaurant). There you can have a beer (3.25€) or mixed drink (9-12€) with nice views of the rooftops of the city.
If it rains (very common in Bilbao), we recommend exiting through Arriquibar Square and continuing along Alameda de Urquijo. Shortly, at number 37, is Twiggy, a pleasant bar with a 1960s decor where you can have a coffee, beer or mixed drink at better prices than at La Terraza.