Can't speak to NYU specifically, but I do have experience with an 1 hour van pool commute. Honestly, even if all you do is take an hour nap on the ride and wake up refreshed to study as soon as you get home, it would still be effective. I found it hard to focus for intense studying on the ride, but as long as it's not entirely wasted time, you're still coming out ahead. I'd usually study in the morning on the way to school, nap on the way back, and be really good about my time management at home...it worked out fine. Plus, like you said, the added time+money bonus of free rent and home-cooked food helps on the time management front too.
Since you live in NYC, you know exactly how the commute is going to work and how long it will be, when you'd wake up, get home, etc. I think putting 2 hrs/day (less productive time that goes towards studying/napping, and time saved not cooking/cleaning) up against 100K+, I would definitely live at home. No question in my mind. I don't regret commuting for 4 years of college at all, and that was for far less savings.
P.S. Like someone above said, you may have to crash on a friends couch every now and again (particularly around mid-terms, finals, other hectic times)...but that's all doable.