Shopping in Chiang Rai is not quite the be-all it is in Chiang Mai. The city does have a small Night Bazaar designed to cater mostly to tourists. It spills out around the adjacent bus terminal at night, at least if it doesn't rain. Unlike Chiang Mai, most of Chiang Rai's market isn't covered, so if it rains in the evening, don't expect most of the vendors to show up.
In addition to the Night Bazaar, there are a couple of hill tribe handicraft centers around town. One is in the Hill Tribe Museum and Handicrafts Shop operated by the Population and Community Development Association. Another is a purely commercial operation out on the highway between the city and the airport.
For a change of pace, you might want to pop into the city's main market for a look. The market sells everything from fruits and vegetables to jeans and housewares. You're unlikely to find anything you want to take home, but it make for an interesting browse.
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