Bangkok is particularly well-known for its plethora of tailoring shops; here you can get a custom-made suit for amazingly low prices compared to the West. Choosing a tailor is tricky though. Tailors in the middle of tourist areas, such as Khao San Road or Nana Plaza, generally provide poor quality and often quote silly prices. Avoid any tailor recommended by touts or tuk-tuk drivers as they cannot be trusted and you'll have to pay their commission; also avoid super-cheap packages or anything done in 24 hours, as the quality will suffer accordingly. The most important rule for getting a good tailor: do research. Don't just walk in the first tailor shop you see, but ask fellow travellers and look online for (user) reviews. In general, the best tailors are slightly off the tourist track in Silom and Sukhumvit.
It will help considerably if you know fabrics and what style you want (bring along a sample or at least a picture), and can spare the time for at least three sessions for a suit (measurement, fitting and final adjustment). Prices obviously depend on the tailor's skill and the materials used, but expect to pay at least 7,000 baht for a two-piece suit. When picking the materials, you're best off with Italian or English cloth as local fabrics are often of poor quality (with the exception of silk). Insist on two fittings for suits. Give the tailor a lot of detail and give yourself time, so you'll get the exact suit you're looking for.