Technically Shrek is part of Production Central, not New York. (Though since they put in the Today Cafe on the *other* side of Shrek and muddied the delineation of the lands in that end of the park, perhaps they're looking to re-work the borders of the lands and expand what "New York" is and rope Shrek into New York.)
The one building that could possibly be used within the current confines of the New York section is one that's currently just backstage to the left of the NY Public Library facade. (You walk past it on your way to a couple of the houses back there during HHN) Based on measurements from Google Maps, that building is only slightly less square footage than the entire Shrek building.
I'm not 100% sure what it currently is, but it has a theater marquee on the front. I think it's used for student groups, etc. Those could perhaps be relocated elsewhere to another building that's farther backstage/not as convenient.
-Rob