If you're looking for game stores, you can find quite a few here, depending on what kinda stuff you (NTSC UC/ NTSC J, etc). I'm not going to recommend any stores selling bootleg stuff though.
For a pretty wide range of stuff for GC, X-Box, PS2, GBA, etc you can check out Seow Choon. It's located at 13 to 15 Jalan Besa. It's actually across the road from Sim Lim Tower as well as Sim Lim Square (which every cab driver should know). It's directly across the road where Sim Lim Tower is on one side and it's on the row of shop houses on the other side. From Sim Lim Square you can walk across the roads in the direction where you see Sim Lim Tower. A word of caution though, they might pull a fast one on you if they think you're gullible so if the price sounds really high you might wanna haggle or just not buy it.

You can find pics here:
http://www.seowchoon.com/catalog/companyinfo.php
If you're interested in older limited edition Japanese game stuff there are two stores I know which might have stuff Seow Choon doesn't. One is Game-1 located inside Hougang Mall on the 3rd or 4th floor. Another is a store I went to once before, it's located either on the first floor in the in the basement of City Plaza (opposite the Payar Lebar train station). I can't recall the name nor do I know if it's still there, but I saw quite a few Japanese Saturn titles there.
If you're going to Seow Choon, you might wanna drop by in Burlington Square and visit I-Con deep inside on the first floor. They have a good range of games too and better prices. Nicer people running the place too.
Don't expect games here in Singapore to be that much cheaper than ordering from import stores in the US, but you should note a few things.
Firstly, most of the NTSC/J X-Box games here are usually in English. They are also MUCH cheaper than their Japanese counterparts and possibly cheaper than the US counterpart depending on the exchange rate. They're locked at 69.90 SGD here, and 79.90 SGD for "special editions" like Otogi 2 (w/ Otogi 1) and Guilty Gear XX #reload (w/ calendar pop-up stand thing). Some games you can get for even cheaper, like MGS2 Substance for like 48 SGD. These games while being coded NTSC/J might also be REGION FREE. Yes this exists, and is very common with X-Box games, although whether they'll region free in the first place depends on the game.
Secondly, if you want Japanese PS2 games, you might want to look for Asian versions, which are much cheaper than the actual Japanese counterpart and the content is largely the same. Unless you're a hardcore collector (which is kind of irelevent for regular games) it's a pretty good deal at 70-80 SGD per game.
If you want more info or advice you can PM me before you leave, I'll try and help if I can.