If you're trying to figure out how housing plays into it, assume that you'd pay about $1000/month in Boston to live with 2-3 roommates (source: I lived in Boston for 4 years). Over 2 school years, that's like $20,000-$24,000 just on rent. Not to mention food, T rides, and all that other fun stuff that comes with being in Boston. Is NYU an extra $20k-$24k more than BU?
It sounds like you grew up in NYC - Boston is a very different city, and perhaps it's worth exploring a new city! I really loved it. I live in DC now and probably won't move back to Boston, but I have very fond memories and several friends who still live there. Boston and NYC are both terrific public health cities, so I don't think you can go wrong with that aspect of it.