I purchased several shirts from the Majestic Suits Taylor's. The quality was good and the price was reasonable.
I stayed at the MG hotel at the time so it was easy. What was nice about the place was that they did not have people out front forcing you to shake hands as you walk by.
I am no so sure you could find better, but I'll give this a thumbs up.
Aside from that I was sitting next to an Indian Taylor on a flight from Taipei to Bangkok and he told me that in Siam Central there were some tailors on the top floor that were quite good and who sold suits that were never claimed.