Where to go in through out Thailand....?

I know the major parts of Thailand I want to go. Like Chiang Mai, Chiang Rai, Bangkok, Phuket, blah blah. Im not sure if I should fly from BKK to Chiang Mai or if I should take a train or bus and stop at places along the way, since I am going to be there for two months, I have time. Are there any places worth stopping on the way north? Or should I just wing it and figure everything out when I get there? I'm having so much trouble planning on where to go while I'm there. I don't want to miss anything but its a lot to figure out. I also don't want to do the normal really touristy stuff... I really want to experience the culture.