Hi,
I have lived in Chiang Mai for a few years now. Chiang Mai is a good place - a wonderful place actually - for both road and mountain biking. My preference is the former, although I've started to do a bit more mountain biking. Overlooking the city is - as I guess you'll know - the mountain of Doi Suthep. The surfaced road winds more or less to the top (a climb of about 20km) through forest, although most cyclists don't go further than the temple (around 11 km). For mountain bikers there is a great network of trails in the forest. Some of the trails are used by Hmong villagers for transporting their agricultural produce. There are books locally available which have mapped out this area for mountain bikers. For road enthusiasts the route round the mountain (the Samoeng loop) is around 100km and involves some pretty tough climbing. Toughest climbing of all in my experience is the ascent of Doi Inthanon, our highest mountain.
As for bikes, when I moved to CM I brought an old bike (a first generation mountain bike) from home. That was a mistake. I could have got a much better bike here for less than the cost of transportation. In the last five years I've bought several bikes which I've listed below with local prices.
Gary Fisher Marlin (I think) 15,000 baht (a few years ago - should be cheaper now)
Trek 3900 (for my wife) 8,500 baht
LeMond Versailles (full carbon road bike) 50,000 baht
In general it seems that prices are a little cheaper here than in my home (the UK). There are also second hand bikes fairly frequently advertised in English language local papers.
There are a number of well stocked cycling shops here. After looking round, and after one misguided buy which I've not listed above, I'm happy with the LSB I use now. He's pretty straightforward and honest. He stocks - as you'll be able to tell - Trek more than any other brand.
There are expat mountain bike groups here. Fewer road cyclists though. I sometimes ride with triathlete friends.
Hope this helps, and whets you appetite for cycling in Chiang Mai.