I would go to the Bay Area, as it seems like you perceive some advantages (climate, industry, etc.) to that route. Interestingly, the rental market has suffered greatly in the Bay Area (while the housing market has remained very strong). This is not the case in Chicago, where the rental market remains fairly competitive. If you can lock in a good 12/24-month rental agreement in SF, it seems like the cost of living will be sustainable with your 60k/yr salary.
Of course, Chicago will always be significantly more affordable--so if you want to have lots of discretionary spending, I would still go to U Chicago.