I was lucky enough to visit New York this time last year.
There are two main magic shops in Manhatten, Tannen's, and Fantasma, and they're not very far from each other. Fantasma is opposite Penn Station & Madison Square Gardens (above the SBarro and next to the Hotel Pensilvania), and Tannen's is round the corner from there, heading towards the Empire State Building. Tannen's entrance is a bit strange though, they don't have a shop front as such, it's a large room in an office type building, up a tiny elevator. See:
Fantasma:
421 Seventh Ave. 2nd Floor
New York, NY 10001
http://www.fantasmamagic.com
Tannen's:
45 West 34th Street, Suite 608
New York, NY 10001
http://www.tannens.com
as for shows, there's Monday Night Magic,
http://www.mondaynightmagic.com at Bleecker Street Theatre, 45 Bleecker Street
New York, NY 10012.
Their last show before a few weeks' break is 22nd September, and it's well worth a visit. Jeff Grow, Master Lee and Simon Lovell are performing that night.
Tannen's and Fantasma are well worth a visit, but Fantasma is a little pricey, lovely shop & staff though. If you're lucky you might bump into the owner, David Roth.
Hope that helps!