The "bay area" in which you are referring is probably limited to downtown SF and berkeley. Anyone with a tidbit knowledge about the bay area would laugh at the your statement if the bay area you are referring includes San Jose, Fremont, Palo Alto, Foster City, or Marin. The comparison you made is the same as, who would pick to live in the filthy slum of downtown LA and skid row when one can live in the luxurious mansions of Hillsborough. Don't include Orange County or SD as LA in your comparison if you are only referring to the city of SF and berkeley as the bay area.
The culture most people think of regarding SF is not that there are nice museums. None of those pathetic SF museams could ever compare to those in Rome or the Getty. The "culture" that most people refer regarding SF is that Chinatown, Japantown, Little Italy, Castro, Mission district (a community of hispanics), Daly City (a community of Filipinos), Union Square and shopping centers and tourist attractions and diners in the downtown business district, Alcatraz, cable cars, Golden Gate bridge (one of modern wonders of the world), the hippy Haight St, Golden Gate park (as famous as Central Park of NYC), the red light district, on and on with the diverse scenaries all within a 15 mile radius. Walk for 30 min and the entire scenary changes from asian to european back to asian. Most people also say Boston has a high sense of culture. It's not the museums in Boston, but the history there that make Boston a "cultural" city.
In terms of political diversity, you are correct in the sense that everyone in SF is rather liberal. However, that liberal thinking translates to encouraging everyone NOT to think alike. Other than thinking alike by being liberal, every other thinking is different. SF, by being liberal as a whole, welcomes those who are radical, or conservative, or moderate, etc. No liberal San Franciscan is going to frown upon one who is conservative. Switch it to the South, and you'll see that the South (sometimes even in Socal) will frown upon radicals and liberals. You will not get the same faces if you walk around with full body piercing or tattoo in SF compared to the South. Similarly, if you are anti-abortion, or Orthodox Catholics, or believes in war, no SFan is going to frown upon you for holding that belief and probably will respect/encourage your individuality. So, I do get your point about the political diversity that almost everyone thinks like a liberal, but I don't think you fully understand the details of the diversified thinking one is encouraged to have in SF.