Pick one OR the other for sure, and get out of Bangkok ASAP... all the travelling around won't let you enjoy the places themselves.
Personally I'd do N. Thailand....
Go further than Chiang Mai....Go to Pai, rent some scooters, then take a few days worth of stuff and scoot to Sappong and stay in the cave lodge for a couple days...they have uber romantic and cheap bungalows!!! Plus the nightly bat/bird show is not to be missed...over half a million of each species fills the skies at dusk!!!
The owner of Cave Lodge provides plenty of information on trekking that can be done without a guide.
You can kyack and raft too, and do a tour of Tham Lod Cave.
Pai is an amazing culturally awsome town. The live music there will blow your socks off.
Chiang Mai is cute but pretty touristy. Spend a night or two and then keep heading to the AWSOMENESS that IS PAI.
Try to catch Chiang Mai on the weekend, the Sunday night market will blow your mind.
DON'T SHOP IN BANKOK...things are waaaaay cheaper in Chiang Mai Night market.
Have funn!!!!!!