Going there in a few days and was wondering what stores I absolutely have to visit.
Stores in NYC
The Tom Ford boutique is nice. I haven't been yet, but I'm sure the Ralph Lauren flagship mansion is nice also, even if it is just to see it. The Brooks Brothers flagship is a nice store, but its going to be the same stuff you can get locally or online.
There are a few good shoe stores, like Crockett and Jones (the only one in the US), JM Weston (if that is your thing), an Alden shop, a few Allen Edmonds stores, and probably some others that I don't know about.
If you are looking for something at a discount, you could visit one of the Century 21 stores.
Keep in mind that NY has sales tax on any clothing item over $110, so depending on what you buy, you may be better off getting the sales associate to ship you the item and avoid the tax.
The one universal recommendation I can give is that if you're into shoes, visit Leffot. A great and very unique high-end men's shoe store.