Italian a Walk away from NYU
Lupa perhaps? It might be too expensive, but I think you can pull off 100 or less for two. It certainly would be my choice (unless you snag a Babbo res). Lupa is a great place to bring a girlfriend.
There's a few around bleeker street that are solid and more affordable. Rocco's would be my favorite. It's got a old-school vibe and solid Italian. It's located on Thompson btw Bleeker and Houston.