I have suggestions on both cities of places I have dealt with.
In New York go to Big City Kite Co. at 1201 Lexington Ave. in Manhattan,
small store but fairly good selection I could not tell if they have a
particular kind of kites on which they specialize but the prices were
reasonable and the owner gets new kites as soon as they are out, but
remember the sales tax in New York is quite high.
I live in Massachussetts and the store I always use is Kites of Boston
which is in Faneuil Hall, 7 North Market (second floor), this is downtown
close to the waterfront and in avery fun complex of stores and
restaurants. The space is very small, actually is more like an oversized
closet but you would never believe the amount of kites in the place they
are all packed in their bags in bins and you have to be ready to open
unroll and examine evry bag and you will find some surprises, they have
all kinds of kites but I would say that their specialty is stunt kites
nevertheless if you don't see something ask for it. I have been surprised
several times with what has come out of a little corner. The guys in the
store are great, know their kites and are very helpful, prices are good,
they always have some goodies on sale so it pays to rummage around and our
taxes are lower than N.Y.'s.
I hope you have a good visit to my city and happy shopping