In the Bronx, there's a decent outdoor cage at Turtle Cove (take 5 train to Pelham Parkway and then take the Bx12 bus towards City Island). They also have mini-golf, or putt-putt, as it were.
Otherwise? Hit the outer suburbs, either Westchester or the Island, and look for Frozen Ropes - you'll have to rent a cage for an hour, but if you're doing it with someone, it's kinda awesome.