This free-spirited city on the bay, which came to life during the Gold Rush of 1849, is one of a kind. Built on 43 hills with spectacular views, colourful architecture, stimulating neighbourhoods, great food and intriguing storefronts at nearly every turn, San Francisco is always pursuing new ideas. Take the California Academy of Sciences in Golden Gate Park, where the 2.5-acre (-hectare) green roof of the new Renzo Piano–designed nature and science museum is covered with 1.7 million plants. Not far away in this delightful urban park are the calming Japanese Tea Garden, the historic Conservatory of Flowers and the copper-covered DeYoung Fine Arts Museum. San Francisco is a walker’s city (although who can resist the vintage cable cars), so it’s easy to plan a day on foot. Start out with shopping in Union Square, the Museum of Modern Art, dim sum and souvenirs in Chinatown, and city views from the eccentric Coit Tower on Telegraph Hill. Always memorable: a cruise and tour of evocative Alcatraz Island.