The Museo Guggenheim Bilbao’s Michelin-starred, modernist, white and ultraminimalist restaurant is under the direction of chef Josean Alija (a disciple of Ferran Adrià). Needless to say, the nueva cocina vasca (Basque nouvelle cuisine) is breathtaking, with multicourse extravaganzas that you'll be remembering (and perhaps paying for) long after you return home.
Reservations are essential. If the gourmet restaurant is beyond your budget, try the museum's Bistró.