I was at NYU from the mid-to-late aughts and Coles, located just above Houston with the entrance on Mercer, was the facility for hoops games. Not sure when it was built. Hardly state of the art (no air-conditioning) but quite large and I don't recall any pillars, lol. When I was there, there were whispers about converting Coles into more classrooms and doing away with sports. I'm sure that conversation comes up a lot at NYU and frankly I don't think it's such a bad idea as there simply isn't much interest among the general student population.
My freshman year, Duke's Lindsey Harding could be seen playing pickup with the guys as she lived in an NYU dorm one summer while interning in Manhattan. I had a friend/classmate who was a decent baller in HS out in Colorado (playing against Ann Strother, Liz Sherwood, the Waners) who was going to join the school team but after watching a game completely lost interest due to the level of play. But she made a heckuva intramural teammate!
Indeed, West 4th Street was always poppin'. I met some awesome D-I girls from NYC and home for the summer break playing there. I did a photography project for an elective class of women's hoops players and they were great. A couple are still playing pro overseas and I believe one is moving up the coaching ranks, currently at St. John's.
Ahh, college nostalgia. I definitely miss The Village, but I'm stuck in some boring provincial town called San Francisco for now :-P. Planning to eventually move back to Manhattan, though.