The best bike shop in Chiang Rai is Fat Free Bikes.  They have a lot of top-end bike and gear for sale, they rent bikes by the day or week, and the prices--given they have no competition--are very reasonable.

Bird, the owner, is a good guy and will steer you the the best value--not the highest price part.  He can offer advice on where to ride and might even hook you up with a truck to take you out of town and up the mountains so you can ride back. (Bird is also the navigator for the Toyota Racing Designs Team in the Paris Dakar Rally!)

The are located in the city center, just a few block north of the Night Bazaar and a block west of the Clock Tower at the intersection of Th. Phahonyothin and Th. Banphaprakan.

Phone: 0-53-752532