The answer can change slightly depending on your personal comfort zone & preferences. But here's my swag at a generic answer. Judging by your profile, I'm guessing you're coming from Washington DC. I'm originally from NYC, so I'll try to frame this from a "big city point of view."

The north-east end of the city tends to be more expensive. North Beach has the lively Columbus Ave cutting through it, with Italian restaurants, bars, and strip clubs. Russian Hill & Nob Hill are more residential and quiet. The Marina and Pacific Heights are trendier and there's good nightlife and restaurants in the latter as well. I believe you can earn the "douchbag" Foursquare badge by checking into too many places in the Marina, if that tells you anything. The population is mostly Caucasian, though Chinatown is right below North Beach.

The eastern center of the city has the Downtown area that has a lot of tourists and a sizable homeless population. Tenderloin is known to be one of the seedier parts of the city. That's here too. Some friends of mine see drug dealings and prostitutes outside their window here. Then south of Market street is SOMA (which stands for, quite appropriately, SOuth of MArket). This district is home to many startups and AT&T Park (Go Giants!). This means traffic can be horrible here, which is offset by the fairly abundant public transportation options.

In the south-east end, we have Potrero Hill, which also has a sizable startup contingent and slightly more affordable housing. Next to it is the Mission district with a large Hispanic population. In the Dot-Com days, Potrero Hill and the Mission were the places to be. Now, they're just a shadow of that. Tons of nightlife in these areas though.

Central San Francisco is the Western Addition, which has a fair community of African Americans. Japantown is smack in the middle of this area too, though oddly most Japanese don't actually live here. There is a lot of low income housing here as well. Below it is Haight, a colorful neighborhood reminiscent of NYC's Greenwich Village in the heyday. The Castro is south of that and is home to a sizable homosexual population.

The southern end of the city is Noe Valley, a bedroom community with a few nice cafes and fairly easy access to highways. Bernal Heights is pretty similar to that description too. Twin Peaks is very hilly and very residential.

To continue this clock-wise movement through the city, next is the south-west portion of the city, where you'll find Inner Sunset and Outer Sunset. Both are very residential and more affordable. Taking a bus from here to the active parts of the city is usually a 30-60 min ride. Inner Sunset has more restaurants and is up against the Golden Gate Park.

The north-west side of the city has Inner Richmond and Outer Richmond. Both are also very residential and again, the Inner Richmond district is the one with restaurants and easy access to the Park. All four of the aforementioned areas has a sizable Asian population. Some even consider a street in Inner Richmond as a second Chinatown. North of these two is the Presidio, a former military district turned residential. You can live here and wake up around trees, hills, and the foggy Bay at your doorstep. Its winding roads make it a delight for bicyclists and motorcyclists, though you'd have to drive out to go to a supermarket. Prices here are usually pretty cheap too.

If you're worried about crime, here's a general guide:
http://sanfrancisco.crimespotting.org/

Finally, here's a fantastic detailed account from Paul Stamatiou about his move to San Francisco:
http://paulstamatiou.com/atlanta-to-san-francisco-moving-cro...

I hope this helps.