My non-experience is that the atmosphere at NYU was much more welcoming to public interest than was the atmosphere at CLS (or Penn, for that matter). It was as simple as speaking to at least one current student who was not going to a firm for their 2L summer, something that did not happen at CLS or Penn (at least not without said PI student having been trotted out especially for that purpose).
And my ACTUAL experience is that when we're talking about the already small PI communities, every little bit (especially raw numbers-wise) helps--one reason why HLS worked for me was that, since the school is so big, you can still get a critical mass of students doing PI, even though the percentage is still small. I think it would have been much harder for me to make the decisions I've made at someplace like CLS or Penn where it really would have been much more a swimming-against-the-current thing, percentage wise as well as raw numbers wise.
My actual experience as a public interest (no applications to firms for either summer) person at CLS is that there are enough people to make a good group of public interest people. I'm not sure if adding 10 or 15 people would make much of a difference. I'm not suggesting Columbia is a better place to go than NYU or other schools for PI, just that my actual experience here and discussions with my numerous friends at NYU lead me to believe that NYU does not offer any tangible benefits to PI people. If that is OP's only reason for preferring NYU, I think it's unwarranted.