Mae Sai (แม่สาย) is the northernmost city of Thailand. It is mainly a stepping stone for visits to Myanmar and has a few attractions of its own. Wat Pha That Doi Wao is an interesting temple complex on a hillside overlooking the border. It has a large scorpion facing (pointedly) toward Myanmar. The market in Mae Sai is marginally more expensive than that across the border in Tachilek, but has a slightly wider range of goods.
By bus from Chiang Rai or Chiang Mai. Buses from Chiang Rai are very frequent (every 10-15 min), cost 40 baht (one way) and take about 1.5 hours, while buses from Chiang Mai take about 4 hours (210 baht one way). All public buses terminate at a bus station well south of Mae Sai, so you have to continue onward to the city proper with red songthaews waiting outside (20 baht per passenger fixed fare). The blue songthaews to/from the Golden Triangle and Chiang Saen, on the other hand, leave from a stand in the city centre a few hundred metres down the street from the border. The last blue songthaew that departs for Chiang Saen leaves at 14:00.