Nikhils:
It might help to know where your meeting is or where you'll be staying in the city. Even with a "full day free," you could spend a fair bit of time just in travel if you're based downtown but want to go pipe hunting on, say, 73rd Street. (The subway is definitely your friend. Don't be afraid of it!)
I'm most familiar with the Midtown area when it comes to shopping/sight-seeing. So I'll also recommend the Barclay-Rex across the street from Grand Central Terminal (which will be easy to get to, no matter where you're staying). I know they carry Dunhills. . . can't recall if I've ever seen Peterson pipes there or not.
Turn left when you leave Barclay-Rex and in a few blocks you'll hit Nat Sherman -- also on 42nd, several blocks west of the Barclay-Rex store, just before you cross 5th Avenue. They may also have Petersons, though I've never looked at their pipes at all.
BTW, you'll sound like a tourist if you call it "Avenue of the Americas." It's 6th Avenue.
Finally, since it sounds like you're looking for a very specific pipe, I'd suggest letting us know what it is. One of us could give the stores a call to see if they have it in stock. Frankly, I think it would be a shame if you spent an entire free day in NYC just looking for a pipe! There is so much to see and do in the city, it would be great if you could get the pipe first thing and then devote the rest of your day to just soaking it all in. (Or, if no one has it in stock, then you could spend your free time just exploring.)
Bob
(Not a New Yorker, but I've visited over two dozen times. . . and I'd love to live there.)