You mention this is for an Intern position. I assume it will only be for a short-duration?
If it is an intern position, I would not worry too much about the money. Yes, your money will go a lot more in Chicago, but an Internship should not be about the money.
I would take the San Francisco job offer because it puts you a lot closer to where the highest concentration of tech people and company are. Use your Internship to learn skills at your company and use all of the other time going to meetups, tech events, socializing, hackathons, etc. Really try to meet (and impress) as many people as you can out here in San Francisco. This will serve you much better.
Source: Quora