There are two elephants in the room here:
1. The exorbitant cost of the Bay Area (and other places like NYC, Boston, D.C., etc.) - there's a reason the Bay Area has the lowest ratio of children to overall population in the country. It's just not an affordable place to raise a family. It's essentially a giant suburbs without the traditional cost advantage of a suburb. You can live in Mountain View, Palo Alto, etc. for the price of living in a world class city like Chicago. You make that choice. Good for you.
2. Where are the grandparents? As someone from a more traditional culture, I don't quite understand the desire for couples to go it alone. Why not live near your parents or have them move to live near you? Grandparent-grandchild interaction is extremely valuable. It helps transmit your family values to your children while allowing your parents to stay mentally active and it also keeps them happy. It also significantly reduces childcare costs.
I'm not married yet and probably won't have kids for a few years but I really think this is the correct AND affordable approach:
*Evaluate where you are in life. There's no point waiting for the perfect time. Adversity is good for kids - it prevents them from growing up to be spoiled brats. I grew up in a Third World country and the only things my parents weren't cheap on were my health/nutrition, safety, and education. That's all that really matters. Have kids before you're too old.
A) If you have a lot of capital or high salary, stay where you are, and have one spouse work part time (can alternate), and suck it up till the kids are in school. Mix in a few days of daycare per week to allow for part-time.
B) If you don't have a lot of capital or a high salary, move somewhere cheap. Your spouse and you can both work full-time and afford daycare a few days a week.
In both situations, have the grandparents around! If you're an only child, it's easy - your parents will be there in a heartbeat. If you and your spouse are one of 2 kids, then your parents can alternate. If you and your spouse are one of 3 or more kids, live near your siblings. Raise your kids around your family.