Do I have to pay taxes for the money that I bring with me to the USA ?

There is no tax on money you already have, except if you gift it or die (gift and estate tax) and then only on large amounts (federal estate and gift tax applies only to millions, while NY State estate tax applies to estates over $1 million, I believe.)  The major taxes you will face are federal and state income taxes (income, not assets - you can have $10 million in the bank, but pay tax only on the interest you earn from it), real property tax (if you own real property in NY), and sales tax on purchases.