Outdoors Gear Shops in NYC proper:
Tent & Trails
21 Park Place, New York · (212) 227-1760
867 Broadway, New York · (212) 255-8889
303 Lafayette St, New York · (212) 680-1938
530 Broadway, New York · (212) 966-8730
2152 Broadway, New York · ( 212) 873-4001
There's also a few Patagonia stores (the Meatpacking Patagonia store is climber/UL-oriented, the other two are more general).
SoHo is a good place for your gear shopping. REI, EMS, Patagonia, The North Face, Victorinox, Icebreaker, Uniqlo, Oakley, Crumpler Bags, Chrome Industries are all right near each other. Uniqlo got some chatter here for some very inexpensive ultralight down jackets a few years ago, not sure if they'll be stocked in August though.
There are also a bunch of cool shops in the outer boroughs like Kamp NY in Flushing, Queens and Gear to Go Outfitters in Park Slope, Brooklyn.