There already is an NYC location open. It's actually the second location they've had in SoHo (the first was the old Vice store on Greene St.)
The current location is on the corner of Broome and Broadway, if I remember right. And yes, it still is open (I was just there two weekends ago). The "flagship" store that they're opening this November is a block or two up from their temp location... walk a little further down Broadway and you should see it on the corner.
Edit: Info from their site-
Address : 486 Broadway, At the SE corner of Broome St. and Broadway
TEL : 212 966-5374
Regular Mall Hours : Mon-Sat: 10:00am - 8:00pm / Sun: 11:00am - 7:00pmwww.uniqlo.com