Its more about where you want to live.

I'm not familiar with the situation in San Francisco. But in Santa Cruz, the cost to own with a 20% down payment is ~50% higher than the rent for the same unit. If you can't afford a substantially higher down payment, you're not really in the market for a home.

With $7k/month after tax, you would probably be renting an 1br, or maybe a cheap 2br. But your income is not high enough to buy anything, unless you start looking for homes well outside the town.