If you're looking for a quieter place to stay that is reasonably central yet just removed enough from the chaos to be peaceful, then Harmony Inn is a good budget choice. Rooms are clean, beds are comfortable, WiFi is free and has reasonable speed. The pool is surprisingly nice. Not much English is spoken, but the young gentleman at the reception was always willing to help us, e.g. arranging a motor scooter rental for us.
One note: The map here shows the wrong location (at least as of February 2015). It's actually a few blocks to the northeast of the displayed location, on Thappraya Alley 11, just east of Thappraya Road.