San Francisco is actually quite a dense, little city, locked in on 3 sides by water and only 47 square miles with 815,000 people (almost three times the population of the entire country of Iceland – fun fact). There are lots of great little neighbourhoods that are only separated by a few meters; its amazing how seamlessly Chinatown turns into trendy North Beach.
Nob Hill (which is barely different to Russian Hill only a few blocks north of it, the other half of the twin peak hill) and the Mission are probably the best neighbourhoods to live in as a young professional or (not broke) student. They’re mostly residential areas, but still within walking distance to anything you’d need.
Market Street east to Pier 1 is a great little area, where the main shopping drag of the city cuts right through the finance/business district, street vendors sell lots of pretty things, Bart stations are all around, and the waterfront facing Treasure Island offers great views of the Bay Bridge and the East Bay. Once you hit the first ferry terminal, you walk north all the way to Pier 39, where another great neighbourhood awaits.
Fishermans Wharf is a super touristy area, starting at Pier 39 where a huge outdoor mall basically sits out on the water, and a great view of Alcatraz can be seen once you reach the end of the wharf. Stinky sea lions bathe out near the boats parked in the marina, and all the shops on Embarcadero sell more or less the same things. The crab stands offer amazing seafood eats for cheap – be sure to try clam chowder in a sourdough bread bowl. And if its a hot day or you want to work off those creamy calories, go for a swim at the beach at the end of Embarcadero.
Chinatown is one of the funnest neighbourhoods to get lost in, mostly because you can actually get lost – street signs and shop fronts are all in Chinese and the only thing you can really read are prices of things. Its amazing how many people don’t even speak english, so you can’t ask what the sign says or directions to where you’re trying to go. But if you let your senses guide you, you’re sure to get some delicious, cheap (maybe unidentifiable) food, buy anything you could imagine at a fresh seafood store (in some cases, still alive), and the dollar-store-like shops sell everything from swords to kimonos and violins to teacup sets, all for really reasonable prices.