Did a little research because I was surprised that this hasn’t popped up yet… only four cities have ever had a championship in each of the four major sports at one time or another…. Shortest time it took each city to win all four:

It took Boston 36 Years: 6 YEARS!!!!!!
(72 NHL, , 05 NFL, 07 MLB, 08 NBA, 2011 NHL)

It took Chicago 25 Years:
(85 NFL, 91-93, 96-98 NBA, 05 MLB, and 10 NHL)

It took LA 22 Years (If you count Anaheim as part of LA):
(84 NFL, 87 NBA, 88 MLB, 06 NHL)

New York currently holds the record with 14 years:
(73 NBA, 80-83 NHL, 86 MLB, 87 NFL)

Also noteworthy, is that Boston is the only city to have defeated the same city in each of the four major sports championships (St Louis):

57 - First NBA Ring (defeating the Hawks)
70 - Stanley Cup (beating the Blues)
04 - World Series (over the Cardinals)
02 - Super Bowl Championship (against the Rams)

There are only 9 other cities that have at least one team in each sport (counting metro areas), but each have never won a championship in at least one sport:

Atlanta - NHL and NFL
Washington - NHL, MLB
Detroit - NFL
Denver - MLB
Miami - NHL (Florida Panthers)
Philadelphia - NFL
Phoenix - NHL, NFL and NBA
San Francisco - NHL (San Jose Sharks, if considered part of the Bay Area)
Minneapolis - NHL, NBA and NFL

Some notes: I counted the Nets as a NY team, even though its a moot point (they have no rings), and did so because they play so close to NYC, and Jersey is so intermixed with the NYC metro area.

Also, I did so because it seems there is consensus that San Jose counts as a San Francisco market team, even though the Bay Area is pretty clear cut: San Jose, SF, and Oakland are all clearly defined. Its not like NY where an outsider can’t really tell Mets from Yankee territory or Jets from Giants territory (primarily because its typically dependent on who your born to, not where you’re born.

So, technically, I’d say for the bay area to win a championship in all four sports and have it stick, the Warriors and Sharks would have to win (obviously), and then either Raiders/A’s, or 49ers/Giants. I would not feel okay with those being mixed, though. In either case, everyone in the Bay Area is just waiting on the Sharks….

And I am even more confused about Anaheim and LA. It seems those also have parallels like Oakland/SF. Okland and SF are separated by water, but only a 20 minute drive. Anaheim/LA are only separated by man-made boundaries, but are a 30 minute drive (all drive times according to google maps).

Also, Anaheim may be getting a basketball team.  If that happened, Anaheim and LA would each respectively have three of the four major sports (each lacking only football). If that happened, would they have to be considered separate, even though one of their teams has Los Angeles in the title? And if LA gets a football team back, would it count solely as an LA team, or could Anaheim piggy back for just that one sport?