I do think that your Trek is a great platform to start with. I have commuted for 8+ years give or take all over NYC, at first on a Cannondale hybrid but as of 2014 exclusively on vintage steel and nice vintage steel at that. Granted at work I bring it inside to a secure area but I do lock the bikes outside all the time. NEVER overnight though and almost never on a secluded street. Even my NYC Kryptonite lock which is truly heavy duty could fall victim then. On the campuses your bike should be fine but do lock both wheels and frame to a sturdy object/stand. I also had a couple of drunks trip over my locked bike on the UWS a few weeks ago as I was partaking in the festive atmosphere of a pub with friends. No harm done.

Welcome to NYC by the way. Perhaps a C&V ride come spring.

Here are my two commuters, the U08 from '14-earlier this year and the Fuji Ace since. Both have been ridden thousands of local miles and tweaked and changed with time and according to my preference.

Unless there is ice, snow or heavy rain I commute year round. Well not today since the the germ infestation led by a household kindergartner and coworkers finally caught up to me.

Untitled by irishbx4th, on Flickr