Depends a little bit on how much you want to spend.
As far as the Indian tailors go, you'll get a decent deal at
Raja's Tailors at Sukhumvit Rd and Soi 4. These guys are aimed at the tourist / expat market and are a volume-driven operation. Expect to pay about $250-300 for a suit, and about 4-5 days turnaround time. There are quite a few Raja's in Bangkok -- the one you want is on Sukhumvit Soi 4 (picture above).
Similar in quality / price is
Pinky's, who I have not used personally but who have a decent reputation.
Most of the Indian tailors are volume-driven and rely on tourists, so be careful that you are clear about what you want and check the quality of the work.
For high-end tailoring, the place to go is
July Tailors. This is a Thai-run tailor who does very good work. It'll take three weeks, but the suit will be hand-sewn and the fabric on offer is of the highest quality. Expect to spend between $1200-1500 for a suit.
Not much in between these two extremes in terms of quality -- you'll have better luck in Hong Kong or Singapore -- and lots of tourist rip-offs in Bangkok, so choose carefully.