Welcome to NYC!
I strongly agree with the suggestion about J&R, completely reputable, prices are pretty good and it's a lot of fun to just wander around. When my father is in town it is usually our first stop . They took a terrible financial hit after the bombing, but even though their retail outlet was closed down for 2 months they still paid all of theur employees and didn't lay anyone off ....since then I have gone out of my way to purchase from them.
Canal near Broadway (Chinatown) has some shops with great prices on Minidisc players, blank discs and headphones.
If you have any interest in Photography you really must try to get to B&H PhotoVideo (it's on 9th Ave and 34th street)....just west of lower Midtown. It is probably my favorite store in Manhattan, carries virtually everything from consumer to Pro for Photo and Video in an incredibly bustling store ...a true NY experience. Closed on Friday afternoons and Saturday, though.
DataVis on 5th Ave around 40th has the best accessories for PDAs, in my opinion.
As the other guys have warned you....stay away from the small electronics stores (tons of them in midtown)....most of them are very dishonest. Oh, the ones near Times Square may be the worst of the lot. Stick with the big reputable stores and you'll do well.
Enjoy yourself, be sure to walk if the weather is decent, it's the best way to see the city. And don't forget to eat....plenty of good stuff all over.
fraz