If mountain access is your primary goal, there are absolutely better options. Salt Lake City comes to mind, where you're literally minutes away from world-class terrain in the Wasatch, or Boulder/Denver. Both cities offer lots of job opportunities compared to the more traditional mountain towns. Boston and Seattle are also options, though they come with their own long drives. And there are other, smaller cities to consider in the US as well.

But SF is unique in that you have a major, cosmopolitan city that's relatively close to a wide variety of terrain and environments, from beaches to forest to mountains, etc. SF is a compromise like any other option, but if you love the outdoors, it's one that gives you a hell of a lot of flexibility while still enjoying the benefits of a large city. It's not Jackson Hole, where the mountains are right there, but no one expects it to be.