First off, you're probably earning more than 115k in the Bay Area.
I moved from Canada and went from $90k CAD to $180k USD. Even with the high cost of rent, I can save more here than what my take home pay was in Canada. I'll admit though that I don't have kids and I don't have health conditions. That would change the equation a lot.
Additionally, the ceiling is higher here. I felt like I was approaching the ceiling in Canada unless I wanted to move to Toronto.