Nearer the top end of the market, I can recommend the Imperial Mae Ping hotel. It's right in the centre and close to the night market etc, but still set back enough to be in quiet surroundings. Staff were brilliant and I really enjoyed my stay there. If your budget can stretch to it, then I suggest a Deluxe Room - they are at the top and give great views across the city
Here's their own website
http://www.imperialhotels.com/maeping/
but I would suggest booking through a travel agent as then you'll get a better rate. Some agencies I have used without problems are...
http://directrooms-thailand.com
http://www.chiangmai-online.com/
The second link will give you lots of information on what to do and see.
Good luck