While in Thailand, I also went to some Magic: The Gathering shops there. They seem to be a bit tricky to find through Google, and the list of shops participating in Friday Night Magic (on Wizards of the Coast's homepage) is at least partially outdated. Here's a list of the shops that I visited, or got confirmed on-site:
Update 2011-01-05: I visited Thailand again this Christmas, and confirmed that Big Magic indeed does lie on the second floor of Union Mall. However, the shopkeeper also indicated that the shop will move to a new (currently unknown) address in March 2011, so the Big Magic entry probably won't be current for much longer. Khun Ple also resided in the same location as previously. I did not visit any other shops.
Gashapon
Gashapon might not strictly speaking be a Magic store, so you're unlikely to find other players to trade card with there, and opening hours may be somewhat irregular (which can probably be said for the other shops as well). However, they do sell boosters of the newest edition available for a reasonable price. I mention Gashapon for two reasons: 1) it's the only shop I know of that can be said to be reasonably centrally located, and 2) it's located in MBK, which is perhaps the most visited mall in Bangkok, and there are also three other huge malls (Siam Paragon, Siam Center and Siam Discovery Center) located near by, so you might want to visit the area in any case.
To get there, take the BTS Skytrain to the National Stadium Station. You can see MBK from the station. When leaving the station, there will be ramps above ground-level by which you can walk right into MBK.
MBK is essentially rectangular, with the Skytrain station on one end and a hotel on the other end. As you will be entering from the Skytrain end, I'll refer to these as the Skytrain end and the far end. Furthermore, at the Skytrain end there are two ramps that you can use to enter MBK. One ramp leads directly into the multiple story Tokyu department store, while the other does not. I'll refer to the sides as the Tokyu side and the other side.
I think the top-most floor of MBK only contains several cinemas. Gashapon is located on the second-top-most floor, which would be the seventh. The correct floor sort of has an 8-shaped walkable area, with some other cinemas in the middle and both ends containing big open areas (holes) to lower floors, with pathways along the outer walls, and an arcade at the far end of the Skytrain end of the floor. Gashapon is located on the far end of that floor, on the other side (i.e. located diagonally opposite of the Tokyu department store corner).
Unfortunately, I don't have the address for MBK, but it's not hard to find.
Khun Ple
The other Magic shops that I visited are a bit away from central Bangkok, so you might not want to walk. Khun Ple used to reside in MBK as well (on the same floor as Gashapon and on the same side, but on the Skytrain end) but has moved and is now the first one you'll encounter if you use the MRT Subway. Khun Ple sells boosters from the newest sets, but also sells some single cards. There are also a few tables for players there.
To get there, take the MRT Subway to Phahon Yothin Station. (Alternatively, if you buy some sort of ticket that lets you travel cheaply on the BTS Skytrain, you can first travel by Skytrain to BTS Mo Chit Station, and immediately on leaving the Skytrain station enter the MRT Chatuchak Park Station. Phahon Yothin is the next station from there, ticket cost 16 Baht.) Khun Ple is located inside the Phahon Yothin station, one floor above the subway ticket gates:
Khun Ple
Metromall in MRT Phahon Yothin
Room 12
Bangkok
Once at the Phahon Yothin Station, also visit...
Big Magic
Big Magic used to reside in the Amarin Plaza shopping mall (which is still worth visiting), near the BTS Skytrain Chit Lom Station, and at least when I last looked, that address is still listed by Wizards of the Coast for Friday Night Magic (but not for the Conflux pre-release). I confirm that it now resides in Union Mall. Union Mall is right next to the MRT Metro Phahon Yothin Station, and one of the station exits does in fact essentially lead right to its door (or at least one of them); you can ask which one from one of the subway guards, and the mall should be visible from other exits as well in any case.
Big Magic usually has products from more than the very latest sets, and might have sales for certain sets. There are folders containing various single cards that you can buy from the shop, and there are also several tables and a fair amount of players that frequent the shop, so you might be able to trade some single cards from them as well.
If you enter Union Mall directly from MRT Metro Phahon Yothin Station, you will ride some escalators to do so, entering in one corner of the building. (The building is essentially rectangular.) Once inside, you want to get up one additional floor, but otherwise stay to the same side of the building (keeping to your right). Big Magic is closer to the far end of the mall than the end where you entered, and is located along the building's outer wall.
Big Magic
Union Mall,
Unit 21-23, 2nd Floor, 54 Ladprao Soi 1
Ladprao Road, Jompol, Chatuchuk
Bangkok Thailand 10900
B-D Shop
Supposedly also reasonably near the MRT Metro Phahon Yothin Station, B-D Shop is listed on Wizards' FNM page as located in Central Padprao Center, and inquiries to players indicated that it indeed resides a bit further along
from Union Mall. However, I never went there, and can't say anything about what products they sell, or whether you can buy single cards there or not, or even if the address I got is correct or not. Be that as it may...
B-D Shop
Central Ladprao Center
Ladprao Road, Under Ground Floor
Unit B25
Bangkok
In addition to these, Card Master, Eternal Magic and VK Shop are all listed on Wizards' FNM list, but I did not visit them, as they supposedly lie even further away from central Bangkok. I also got some information about some shop in the basement of Century Shopping Mall
(probably Century Plaza, near the BTS Victory Monument Station) but without even a name of the shop it did not seem worthwhile to hunt it down.
If anyone can confirm these, or other shops, feel free to chip in.