Valencia

Valencia rewards the traveler who mixes eras without apology. In one morning you can stand under the ribbed stone vaults of a 15th-century silk exchange, climb the bell tower of a cathedral that claims to hold the Holy Grail, and haggle over tiger nuts at a modernist iron-and-glass market that has been open since 1928. A free walking tour is the fastest way to make sense of it: Roman Valentia, Moorish Balansiya, and the medieval trading empire that built the historic center you're walking through.

Then there's the Valencia that looks forward. In 1957 a catastrophic flood convinced the city to reroute the Turia river outside the urban core, and the dry riverbed became the Turia Gardens, a nine-kilometer green spine that ends at Santiago Calatrava's City of Arts and Sciences — a cluster of white, bone-like buildings that looks like nothing else in Spain. Add the birthplace claim on paella, the sweet chill of horchata on a summer afternoon, and a beach a tram ride from downtown, and you have a city built for slow exploring.