The celebrity chef picks his favorite spots for shopping for the best ingredients.

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Mercado Central, Valencia
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Mercado de Abastos de Algeciras, or the Mercado Torroja (Plaza de Nuestra Señora de la Palma, Algeciras) is named after the engineer Eduardo Torroja Miret. The market is an architectural breakthrough—definitely try some fried fish with a glass of Manzanilla early in the morning in the little stalls that serve it.

Mercado Central, Valencia (Plaça de la Ciutat de Bruges)—If you go here, you must visit Central Bar by Ricard Camarena.

Mercado de la Paz, Madrid (Centro Comercial La Paz, Calle de Ayala, 28): You can find here the best tortilla de patata in all of Madrid, at Casa Dani, one of the stalls in the market.

Mercado Dominical de Quesos, Asturias: A market specializing in cheeses—go here and taste all of the cheeses, and bring some home to share with friends and family!

Mercado de Nuestra Señora de África (Avenida San Sebastian, 51, Santa Cruz de Tenerife, Tenerife): Go here to buy papas negras—some of the best potatoes in the world—grown in volcanic soil.