Before this thread I thought bay area might be 100k - 120k and cost of living / uprooting the family wasn't worth it. Also worried about the competitiveness of the market out there for software engineers.
If you buy into the idea that where (and with whom) your children go to school will heavily influence their success/happiness, you'll find yourself choosing between expensive-area public schools and expensive private schools.
Most of the public schools in California are pretty crappy (and the bay area is no exception), and to get into the ones that are good (by some measure), you have to swallow either huge rent or a huge mortgage so you can live in their area.
There are some good private schools, and you don't have to live in super-expensive areas to send your kids there, but aren't there excellent private schools outside the bay area / in lower cost-of-living areas ?
For your particular situation, you may find that the math works out to stay in the midwest. Additionally, that's just the raw numbers; there are lots of "intangible" factors that favor the midwest over the bay area, especially if you have any kind of roots there.
But honestly, it seriously depends on what technologies you have experience with.
But to give you a number, you could very easily get $125k. I bet if you somehow got 100 offers, the vast majority of them would be normally distributed between $110 and $140k.
Mitigating factors: 1. The universe of companies willing to fly-in a candidate and pay for relocation is smaller, so you have less bargaining power. I was able to secure a 20% raise the first time I changed jobs here -- a year after relocating.
2. If you have impressive skills in more lucrative technologies you can certainly make more.
I talked to 2 companies in Atlanta in 2010ish (MailChimp and a smaller private company) and their salary ranges were well below that ($90-110k iirc). I'm surprised to hear it's so high!