I haven't been there for a few years, and there was talk of this place getting torn down, but in Taipei, Taiwan the best place is near the intersection of Chung-Hwa East Road and Ba Teh Road. Not 100% sure if that's the correct Romanization because I just always said it to a taxi driver or took the bus. The Chung-Hwa East Road is the one that runs in front of Taipei main station. The intersection I'm talking about is only a few minutes away by bus. Bah Teh Road is actually a diagonal road so it intersects Chung Hwa East Road first. If you get off at the original intersection I said (Ba Teh Road), you actually have to walk a bit down the street, but Ba Teh deadends into Chung Hwa so you can only go one way down Ba Teh (away from Chung Hwa).
It's a bit closer if if you get off the taxi/bus at KDM Hotel right on Chung Hwa East Road (but I don't know that cross street name). Anyway, from KDM Hotel you should head towards the underpass beneath the roadway.
The stores are in several old buildings around there, but the main one is hard to miss and has a few floors. Go up the steps (or down) and this stretches a ways back directly underneath the roadway above. In this entire few block area, they sell lots of computers & parts, but also a fair amount of video games (and books and videos). There's another really good place in a 4 story building in the main shopping district, but I would have no idea how to tell you to get there. I just get off at the McDonalds near the entrance to the shopping area and walk there (many turns!). Hope that helps... please report back if you found it (and if it's still there!).