Obviously the Bay Area is an obvious place for a major American city, but why is San Francisco specifically the most important city in the region? Looking at a map, there are several spots in the East Bay especially which would seem like equally strong contenders, especially since that side of the Bay is significantly easier to connect to the rest of the U.S. with rail.
Vallejo especially seems like it has a near optimal location--at the mouth of the Straits of Carquinez (so super easy access to the Central Valley), but also on the bay, so easy ocean transport. And it was in fact a city of some importance in early California. Why didn't it (or Oakland, or Richmond) become the big dog in the region?
It's funny you mention Vallejo, as its neighbor Benicia was SF's main initial rival in the Bay Area, even serving as the state's capital for about a year. Benicia had a much better natural harbor and more temperate weather.
It seems SF won out as much as anything due to having a head start, primarily for religious and military reasons. The first settlement of the Bay Area by Spanish Franciscan priests was in modern SF to better control the entrance to the Bay and thereby sea access to all of central California. After Mexican independence, the Mexican government established large ranches for military officers near the Franciscan mission. The entire area was seized by the US military during the Mexican-American War to again control access to the entire Bay, and an American military installation was built in 1846. There was a Mormon colony established there the same year, and the town pulled a minor coup by stealing the name "San Francisco" after the Bay just ahead of Benicia trying to do basically the same in 1847.
When the Gold Rush began in 1848 and the Bay Area population skyrocketed, the natural first port of call was San Francisco as it was by then the largest settlement in the Bay, even if not yet more than a thousand in population. But by being the largest, it attracted the majority of those arriving, further separating itself from its competitors, increasing the appeal of further settlers, creating a feedback loop. Soon, it was simply too large for somewhere like Benicia to catch up, even with wealthy industrialists supporting Benicia's cause.
Basically, San Francisco won due to first-mover advantage and increasing returns to scale.
