The NYU Nerd
If she's an undergrad, you're clearly not in this for romance. I'd send you somewhere within stumbling distance of her dorm room. West Village it is. You'll also want to go somewhere that offers familiar comforts, to avoid any potential confrontations with her (likely) unpracticed palate. I'm thinking a place that takes something she knows, and elevates it to stratospheric heights. Let's say pizza. And better yet, let's say Keste. Its pliant, blistered crusts and melting pools of fior di latte mozzarella are as close to the platonic ideal of Neopolitan pizza as can be obtained in this town.
A graduate student is another beast entirely. In this case you'll want a place that's quiet and languorous, such that she can feel confident in holding forth about blood borne pathogens, or dramatic writing or child development or whatever noble or ignoble educational path she's chosen. How about Northern Spy Food Co. (511 East 12th St.)? Seasonal American, lots of locavore buzzwords, simple, accessible and affordable. Crack a bottle of hard cider to keep her bon mots flowing while you think of something clever to say.