Please be aware that you don't have a lot of (or any) power in this situation.
You need to a realize that most companies hire interns for one of several self serving reasons:
- it's a convenient tax break (in some places)
- community outreach type of approach (makes them look friendly)
- they have a lot of simple, repetitive, cheerless, and thankless tasks that they need someone to grind (like performing some very basic testing, or organizing files on their internal wiki)
- there's a small chance that they might find a talented person who will come back to them as a full time employee
- some combination of the above.
You are not expected to bring a whole lot to the table. The position marks you - by definition - as the lowest man on the totem pole. For most employees you're only going to be the guy who sits in a corner for 4 months and doesn't do much of anything.
Granted, some companies value their interns a little more, and actually throw some tasks at them, but in any case, you're not expected to make a splash, save the department, or otherwise perform any admirable tasks.
That being the case, why would the employer negotiate with you? They have a whole list of students who would probably perform just as well as you in the limited role of the internship. As far they're concerned, they're doing you a favor.
If I were you I'd keep my head down and strive to get the job which will give me the biggest opportunity to learn, or at least who's name will look best on my resume. When you have 5+ years of experience under your belt and have specialized in a number of technologies, etc. then you may be able to negotiate your rate with a company which really needs your skills.
Right now you're most likely to be dismissed for trying to give them an ultimatum.
Edit For clarification:
Unless you're the teenage version of Bill Gates, and have companies such as Microsoft, Apple, and Facebook fighting over who gets to have you, you will most likely not be able to negotiate a salary increase.
You can point out that the offered pay will make it very difficult for you to afford housing in that city, and they might offer you some sort of aid, but most likely they'll just say "tough luck, are you accepting, or not?".
At that point you may very well end up stuck with whichever offer you can afford to take. It's not fair, but such is life, I'm afraid.
I strongly advise against any sort of trying to get these people into a bidding war for your services. It will most likely get you nothing other than a bunch of rescinded offers.