I live in Berkeley, which is right across the bay from San Francisco. The two cities are connected by the mass-transit system called BART through an underwater tunnel. My perspectives on San Francisco are thus somewhere midway between that of a tourist and that of a local. In this writeup I'll discuss my favorite areas of "The City", as San Francisco is known in the Bay Area.
North Beach
North Beach is my favorite place in America to hang out. North Beach is an Italian section of The City that has been called "The soul of San Francisco." It was home to Beat writers during the Beat Generation. At the south end of North Beach is the ultraliberal City Lights Bookstore which was a haunt of famous author Jack Kerouac and poet laureate Lawrence Ferlenghetti. The heart of North Beach is Columbus Avenue, along which dozens of outdoor cafes, bakeries, and slightly more upscale (but never snobby) restaurants are lined. Every year in late July and early August North Beach hosts a jazz festival. North Beach is adjacent to Chinatown, Fisherman's Wharf, and the Financial District. The nearby Coit Tower offers panoramic views of the city and the bay.
North Beach is very popular among locals because it offers cheap, casual places to dine, relax, read, and converse. Two of my favorite hangouts in the area are Café Puccini and Café Greco. Café Puccini is a crowded cafe with an operatic ambience that serves great espresso and Italian snacks. It's incredibly cheap--for about $1.50 you can get a plate of warm focaccia covered with delicious pesto and scallions. Next door is Café Greco, which I enjoy almost as much. One time I ordered a bagel with cream cheese there for about $1.50, and didn't expect much. I got a scrumptious bagel with cream cheese and slices of tomato that was drizzled with extra virgin olive oil and sprinkled with fresh oregano. All of the cafes in North Beach are of such high quality. Perhaps the best espresso is served at the quaint Caffe Trieste.
Haight Street
Haight Street was famous in the 60s for being the center of hippie culture. Today it still has some hippies though it has gotten trendier--there's a Gap clothing store there. The intersection of Haight Street and Fillmore Street is a great location with excellent cafes and a famous beer bar, Toronado. Toronado has some of the best beers in the world on tap and in bottles. Fillmore's Cafe is a great place in the area to get internationally-influenced snacks and drinks.
A little ways up from Fillmore Street is Buena Vista Park, which is relatively little known. Buena Vista Park is built into a very high hill from which you can get incredible views of San Francisco and the bay. The winds up there can get very chilly so bring a jacket or sweater.
Further up Haight Street, at the intersection of Haight and Ashbury streets, is the epicenter of hippie culture. There are clothing stores where one can buy tie-dyed shirts, head shops that sell drug paraphenelia, and psychedelic music shops. It's not my favorite place to hang out but it's worth seeing.
Golden Gate Park
At the end of Haight Street is the fabulous Golden Gate Park. Golden Gate Park is a lush, well-kept park with lakes, gardens, and museums. It is larger than Central Park in New York City. One highlight of the park is the Japanese Tea Garden, an area with intricate paths, ponds, sculptures, bridges, and a teahouse. There is a lovely botannical garden and a naturally-formed island in a lake which has a hill for viewing the park. Some of the other noteworthy sights in the park are the California Academy of Sciences and the deYoung Museum of Classical art. If you start from Haight Street and keep walking for miles north through the park, you'll eventually get to a beach on the Pacific Ocean side of the Golden Gate Bridge. This is quite a nice end to a walk through Golden Gate Park.