HAHA, some of these suggestions are absurd for a "poor college student"
Well first of all, bring your id, since many museums offer discounted admissions.
The Metropolitan Museum of Art is indeed not to be missed, it has a bit of something for everyone:
The MoMA in Queens is an EASY subway ride away (while their home in Manhattan is being rennovated) if you are into more modern art
Of course Times Square is cool for people who have never been, I suggest not coming during business hours, as you will invariably be yet another body on the sidewalk and make me have to elbow you out of the way
kidding, but the lights do look cooler at night.
If you wake up early enough you can see Good Morning America being taped in times sq. http://www.abc.com
Of course, take a walk around lower manhattan, checking out the ground zero area, and walking along Wall St, seeing the oldest Church in American (I think) at Wall St and Broadway. The stock exchange down there too, and either hit Battery Pary or the South Street Seaport for a nice walk along the water. Across the Brooklyn Bridge in Brooklyn is the Promenade from which you have a most splendid view of lower Manhattan.
SoHo and TriBeCa are two neighborhoods that are cool to walk around. SoHo moreso, and yes, the walk along W Broadway (DIFFERENT from Broadway) is great because it is quintessential SoHo, though Broadway is cool too, just more crowded. You can also find cheap eats around SoHo.
For going out on the cheap, and eating on the cheap, I'd suggest the East Village for college kids. Its fun, its dark, its moody, its college types and fun. This is everything east of Broadway from Houston St up to 14th St.
For any other questions, feel free to ask via email in my profile.