Remember that they'll talk to your line manager and read your performance appraisal.
I have decided to intern somewhere that is hiring, that intends to take on all of its interns if they're good enough, will be on one of their number one desks, and one that is very respected in the industry. Should make the job thing slightly easier (fingers crossed).
I went for a Bulge Bracket this summer and already have that on my CV, so I choose my bank due to the above combination.
I got some rejection from some banks. However, my situation is fairly unique (I'll have done two summer internships by graduation and a few have asked me to keep in touch and are asking me to apply full time. I guess that means banks are happy to look at people again.
If you got to interview stage, think about the feedback - make sure you can't get rejected for the same reason.