So you're interested in shopping for games? There are an innumerable number of Gamestops along Broadway but I'm sure you're looking for a more interesting store. My favorite place is
J&L Game Trading in Chinatown. They have a huge selection of imports and rarities. A bit pricey, but not much more expensive than the chains. There is a subway stop nearby that's marked on the map. Nintendo World wasn't all that special, the decor is nice, but I wouldn't exactly shop there for my games.
The best shopping to me is downtown Broadway, from 14th Street/Union Square south to Canal Street. Walk down this section, keeping a sharp eye out for stores that interest you and you'll be set. As you exit the station there is a Virgin Megastore that is so much better than the one in Times Square if you need music/movies. A good starting point is
Strand Books, which is my favorite bookstore, with
literally miles of bookshelves and great prices. Across the street is Forbidden Planet, which is a huge comic book shop. Stay the hell away from the Manhattan Mall or Midtown in general if you want any shopping done, it's crowded, noisy and just unpleasant to visit.
As a lifelong resident, the idea of taking a taxi around Manhattan is complete insanity. For the price of a $7 Fun Pass, (unlimited subway/bus rides for 24 hours) you can barely get crosstown at busy times. Don't worry about the subway, it's very safe and reliable. I ride it everyday and have never been accosted nor run into smelly stations. I'd advise you to look at the map that's posted at
The MTA Site. This online version is actually very shitty, as it does not have the major streets written down nor neighborhoods marked, so glance at the PDF. I will admit, it is quite overwhelming at first, especially in Manhattan. But think of each North-South avenue as having a subway line under it, with a few East-West lines that go crosstown.
I'm going to assume your starting point is Times Square, which has nearly every line connection in Manhattan. If you want to go down to Union Square, which is my advised starting point, take the N,R,W downtown to "14th Street-Union Square". You can just walk down Broadway from there and find all the locations I've marked.
It would take a huge post to go over all the places I like to eat at, so I'll just list my favorite place in Manhattan. My other choices are in Queens and Brooklyn, and I don't know how that would work out on a first trip to NYC.
Pho Bang. I can never get tired of this place, it doesn't get any better than authentic Vietnamese food if you're sick of all the Thai places that permeate the city. It's incredibly cheap, filling, and bursting with flavor. My favorite dishes are the Banh Tap (appetizer, pork loin on shrimp chips with a dipping sauce) and Tai (Pho, basically a beef broth with noodles, bean sprouts, beef).
Phew, that's all off the top of my head right now. If you have any questions feel free to ask, it'd be a pleasure to help. :D
Jam it back in, in the dark.