No. In the specific case, NY sales tax is not refundable.
In the slightly more generic things labelled as "sales" taxes are generally not refundable. Taxes that work as "value-added" taxes often are.
The VAT in many European countries (as noted by Zephyr in comment to the question above) is refundable, as is the GST (Goods and Services Tax) in Canada.
The taxes are designed by the government to cover different items at different stages of the production chain, which helps to account for some of the discrepancies.
I travelled by car to Plattsburgh, NY on the weekend. I purchased a set of hand wrenches at the local Sears store and, of course, paid the NY state sales tax. When I returned to Canada I was a good citizen and declared my purchase. I thought that I would have to pay GST + PST on the price of the tool set. But no, I was charged on the total price shown on the bottom of the sales receipt which included the NY sales tax. I complained, saying that I was paying tax on top of tax and in the case of the Quebec PST/TVQ, tax on tax on tax. The Canada Border Services agent said "too bad, we charge on the transaction total".
In other words, their assement is on the total you paid to the merchant regardless of what you bought. For example, let's say you went to McDonalds and bought a $20 meal for youself and your wife and a kid's $2 toy (for your nephew back in Canada). You ate the meal at the McDonald's and kept the toy. When you got back to the Canadian border you declared the toy and showed them the receipt. You would be charged GST & PST on the total price of $22.
Im a british citizen, will be travelling to nyc for holiday. In the Uk if something is selling for £5 you pay £5 at the till, but in the USA its not like that as they add sales tax or VAT, not sure which one.... as a tourist am i exempt from paying the tax or can i get a refund after my holiday? Also whats the difference between sales tax and VAT in the USA?