There is great advice on this thread, and woodsorrels guidence is excellent. Have a look at Outdoor Magics threads as well, becuase this question comes up every so often. I found this oldish thread -
http://www.outdoorsmagic.com/forum/gear/outdoor-shops-in-new-york/19773.html
Dont forget more general shopping. Clothes are often much cheaper, especially if you find the clearance dept or a whole outlet (Century 21, etc). Of course dont make my mistake when my wife and I went on honeymoon of buying cheap Levi's in one size, only to find with the huge food portions that those trousers were never going to fit again. Luggage might be another one. I've just looked at Travelpro luggage (a favourite with cabin crew) - buying a 29in case from the UK stockists costs £350, whereas the same thing from an online US store (so will deliver to US addresses free but seldom international) is $255. Thats £164. So even if you dont go into a store, you can still shop and have it delivered. And your probably going to need another bag anyway - we certainly did. And my wife loves her Westin travel blanket. We bought it via Amazon and it cost us about £46, but its $59 (£38) from the US website.
As others have said, do your research. If you go into a store and only look for brands you've heard of in the UK, you might miss some real bargains (I know I did) - Kenneth Cole suits wree stupidly cheap when I last went, but at that time, wasn't a brand I'd even heard of.
And dont hesitate - your not going back to that store, so if you see it, buy it. Should have got a 2 for $X deal at Sketchers (why did I need two pairs?), but didn't. Most comfortable trainers I've ever owned, and vastly more expensive here. And totally regret not getting an M65 jacket back in 1989 when I was in a NY thrift store - they had about 5 and I didn't even think about it.
As for knives - there is a guide here:
https://www.gov.uk/import-controls-on-offensive-weapons -
What they are happy with is a bit of a grey area, and whether you put it in the hold or on carryon is even worse (I doubt carryon). I had to fly to/from Inverness twice in the last two weeks, and they patted me down twice, even though there was nothing on me. Knives on Transatlantic flight might be much worse. Perhaps better to get someone to send it with full declaration, etc?
Have fun in NY. Our recent holiday in Scotland got semi shot for various reasons, and I'd love to take the family to the city as a replacement trip, if only for the food.
BTW - Seatguru is your friend!
