You should only fly people out if you are strongly considering them. You're going to pay this person $20-$35/hour all summer, what's $300-400 just to make sure they are exactly what you want?

You do not have to fly people out, Google/hi5/Ning don't seem to do this but Slide/Facebook still do. It's clearly how convinced you and your team are of this person. You can try and make video conferencing part of the phone screen process of course.

I am no expert on how interviews should be done and it depends on the kind of intern you want: Someone who can learn fast? Someone who is already skilled with your stack? Someone purely motivated?

Ideally all, I'd pick one and base your questions accordingly. Companies I mentioned above let potential hires code in any language and simply check that they know the fundamentals: recursion, data structures. Gauging their passion/motivation/drive is done through their resumes and side projects like others have mentioned.

My personal opinion, you want to pick someone who is capable of learning most things without asking you otherwise it's going to be a struggle of he/she constantly asking you questions.