I have only read some of these replies, and the ones I have read don't seem to be giving you very good advice (I apologize if someone did leave some legitimate advice that I just didnt read).
Here's my advice coming from someone who was a culinary student, and like you in the beggining of my carreer was intimadated by high end restaurants.... I have since worked in several high end restaraunts as a line cook, was sous chef for upscale hotel for several years and am now Exec Chef and F&B Director of a conference center.
Go in suit pressed and dressed to impress. Have resume ready and ask to speak to the Chef, if he is not available ask to speak to any manager present. Explain to them your situation and express that you want to learn, I have always been more likely to hire someone with less experience if I can honestly believe that they want to learn and will put everything they have into it. Be prepared to have to settle for less pay and to be stuck on garde manger. But if you can get into a upscale place try to ask questions and watch as much as possible, everything one chef does will not be the same with another chef. This is another thing to keep in mind you will learn a lot of "right" ways to do things but seeing the "wrong" is just as important in your professional development, but if you see things you think are wrong keep your mouth shut because that's a quick way to get on the chef's bad side.
I hope this helps you a bit.... oh and make sure you go into restaurant between 2-4PM that's your best chance to actually have the opportunity to speak to someone.