Bernal
Fun enclave up on Bernal Hill just south of the Mission. Phan lives there. Pretty good food, and you're just up the way from the Mission. Depending on where you are, there's a small section of Bernal that sort of bleeds into a rough-around-the-edges part of the Mission, so beware while AirBNB'ing.
Castro
The gay epicenter of SF. Fairly centrally located to a lot of good SF stuff. Very gay. Pretty safe. Parking is difficult but not impossible. Food is mediocre but close enough to good food in the Mission and Hayes Valley. Public transportation is pretty easy here.
Chinatown
Fun for a visit, but I wouldn't want to stay in Chinatown. It's kind of a mess. The food is disappointing.
Civic Center
Probably too risky for AirBNB. Might find a nice condo or something, but more than likely you'll end up in some dirtbag Tenderloin/SoMa/Western Addition flophouse. Do not want. City Hall and the Asian Art Museum are beautiful, though.
Cole Valley
Quiet little neighborhood tucked away by the Upper Haight (that's Haight-Ashbury to tourists). This is a fine Air BNB option. Parking difficult. Public transportation is average. Some OK food options near here or on Haight.
Cow Hollow/Marina
OK, the cons: Very preppy/douchey, food is mostly mediocre. The pros: Parking not horrendous. Basically no hills. Very safe. Walking distance to the water, views of the Golden Gate Bridge, could walk to Ghirardelli Square or Fisherman's Wharf if you really want to go fannypack tourist mode. Public transportation only by bus. This wouldn't be the worst place to find an AirBNB.
Financial District/Union Square
Meh, don't stay here, unless you really like malls and want to be near Union Square. Mostly dead at night. A few nice expensive restaurants.
Fisherman's Wharf
As touristy as you can get in SF. Chain restaurants galore.
Haight-Ashbury (Upper Haight)
If you're really into that whole Summer of Love vision of SF, go here. Just be prepared to be accosted by strung-out, grumpy, homeless teenagers.
Hayes Valley
Parking is very difficult here. Big hot spot on the SF restaurant scene. Kind of wedged in between some not-so-nice neighborhoods, so it's definitely got some rougher edges. But it's one of SF's great new booming neighborhoods. Good location close to the Mission and the Castro. Decent public transportation.
Sunset (Inner or Outer)
Pretty far out of the way. That's a major, major con. Pros are great Asian food, proximity to Golden Gate Park (SF's answer to NYC's Central Park), relatively easy parking. If you go way out to the Outer Sunset, you'll be close to the Pacific Ocean. But public transportation here, especially in the Outer Sunset, is horrendous. Must drive while staying here, or prepare for hourslong bus rides.
Lower Haight
Some decent places to eat and drink near here, but fairly quiet. Some parts of the neighborhood are not so nice.
Mission
Best food in SF. Hipster central. Some parts are really very nice and some parts are pretty sketchy. Parking is OK. Public transportation is OK but can be sketchy. Find a place west of Valencia and let's talk.
Nob Hill
Old money neighborhood in SF. Way up in the hills. Pretty decent location to tourist stuff in SF. Parking is horrendous. Public transportation not so great; only bus. If you want to do the whole "I'm up in the hills in SF" thing, it's an OK option. Beware of staying too far south in Nob Hill. Then you get into the Tenderloin, and unless you're looking for hard drugs, transexual prostitutes or decent Vietnamese food, you don't want to be in the Tenderloin.
Noe Valley
Quiet semi-suburban neighborhood west of the Mission and south of the Castro. Public transportation is decent. Parking is decent. Not the most convenient option, but location near the Mission is a plus. Very safe here.
North Beach
SF's Little Italy. Convenient walking to tourist stuff in SF. Food is meh, although there are a handful of gems. Parking very difficult. Public transportation is meh; bus only.
Pacific Heights
Home to the wealthiest of the wealthy in SF. Fillmore Street is kind of nice; lots of boutiques. Similar neighborhood to the Marina/Cow Hollow minus the fratsters. Perfectly fine place for an AirBNB. Safe. Parking is meh. Public transport is bus-only. Not so convenient to tourist stuff. Would probably only be worth a look if you plan to drie while in town.
Potrero Hill
Nice, quiet neighborhood that's close to nothing. Car is your only real option. Better for residency than tourism.
Richmond (Inner or Outer)
Pretty much echoes the comments about the Sunset (the Richmond is north of Golden Gate Park; the Sunset is south). Only difference here is that there are more food options in the Richmond, but the public transport isn't nearly as good.
Russian Hill
Sandwiched between Marina/Cow Hollow and Nob Hill. Kind of hilly. A nice stretch of shops on Polk Street. Fairly close to some tourist stuff. Not a bad option for AirBNB, but it's case-by-case.
SoMa
Sprawling neighborhood south of the FiDi, east of the Mission and west of the Bay. Stands for "South of Market" Street. There are some pockets here that are really nice, and the neighborhood is being developed like crazy, but there are just as many pockets of sketch here, so I'd avoid. Some good food, though.
Telegraph Hill
Near North Beach. Has some famous parrots and Coit Tower. Very close to tourist stuff. Very hilly. Parking is terrible. Public transportation is not so great. Put this in the Russian Hill-Nob Hill-North Beach group of similar old neighborhoods up in the hills.
Twin Peaks
Best views of the city, but you're way, way up on SF's tallest hill. Not convenient. Public transportation is comically impractical. Close to Noe Valley/Castro, I guess.
Western Addition (NOPA)
Gentrifying area that many are pegging as the next big thing. Some decent food here. Close to the Full House house (The Painted Ladies). Be careful, though, as there are a fair amount of housing projects close by, too. It's block by block. Definitely check with us before pulling the trigger here.