A very common place to go for a "visa run" from Chiang Mai.
Mae Sai, or the whole 'Golden Triangle Loop' of Mae Sai to Sop Ruak to Chiang Saen and back. Mae Sai is known as the 'northern-most point in Thailand.'
There is not much to see in mae Sai. Its mainly a place to shop and look across the small stream which separates Thailand and Burma (Myanmar). Unless there is one of the rare "flare-ups" along the border, westerners can easily cross the bridge into Tachileik, Burma on the other side of the stream.
However, there's not much to do in Tachileik except shop and you're only give a one-day visa to enter. It does count as a official exit from Thailand. So be sure if your an expat or on a retirement visa you have a re-enter or multiple entry visa. This is not a place where you can enter into Burma for onward tourism.