I don't think there are any good ones in the phuket area. There's one in Bangkok that's used by Western diplomats and the likes that is supposed to be ok, but it's also not as cheap and doesn't work as fast as the more touristy ones (I believe its called narin). Bear in mind that the house style in Thailand is a bit different than we're used to, and most suits will be fused. Narin does full canvas.
If you're willing to take a gamble that could result in an unwearable suit you could give it a try, but I wouldn't do it. Make sure they use British/Italian fabrics, as I've heard a lot of them tend to sell poly blend fabrics as all wool.