I go to NYU, and personally I feel uncomfortable holding nice bags in the City. Maybe it's just from listening to my worried mother all the time but I wouldn't risk the extra paranoia...especially if you need to use public transportation. I like to use my Marc by Marc Jacobs bags because they're very "discreet" and they don't cost as much as LV. That's just my opinion though, I guess it all depends what your preferences are!
On lighter days and once spring comes I plan on using my Neverfull MM (but thats not the reason I bought it) and everyday I use my Longchamp le pliage shopping tote, the biggest one. Honestly, its the best school tote out there, SUPER durable, cute, VERY lightweight, not at all flashy/logo-ish, I love it!