You will more than likely need to fly into BKK. I would allow 2 days to get over your jet lag and check out the sites.
Fly up to Chiang Mai or if you want to save a few $$s you could get an overnight sleeper train. check
The Man in Seat Sixty-One...
Chiang Mai is a great city, Sunday walking street market, Tiger Kingdom, zip lining, elephant camps, cooking schools...the list goes on and on. I would allow 4 days as a minimum
Finish off your holidays with some beach time in Phuket Direct flight from CM with AirAsia is quite economical.
Back to BKK for your flight home and any last minute shopping.