I don't get the thing about cost of living. New Haven is not expensive, neither is NJ commutable to Princeton, nor Philadelphia. Chicago's cost of living is right at the national average. Durham's is probably below. Etc.
In short, our university appears to be doing everything they can to extract money from their graduate students. It is ridiculous and nearsighted.
Yes, if you're single, you'll probably need roommates, but it is definitely doable.
If you want to insist on a private apartment, grad school isn't the place for you.