The only arcade that I liked in Times Square was on 42nd street called Broadway City. However, I have noticed that 42nd street itself attracts a different kind of crowd of people the then the rest of times square does and it can be a problem. It closed a few years back after there was a shooting there and the BBQ resturant took its place.
The problem with a place like Dave and Buster's or the ESPN zone for that matter is that yes, you can enter if your 18+ or with someone who is. But, they give you strange looks the entire time.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll