Spend 3 days in BKK and the rest in Chiang Mai. You can see all the places in BKK in 3 days - all the Buddha temples, Foating market etc. Chiang Mai has many places to trek and is very quiet compared to BKK. Look up travel guides like Frommers and Lonely Planet. Come back to BKK one day ahead to do your shopping (you don't want to lug all that stuff to CM, do you).

Bayoke Sky hotel in BKK should fit your bill for Thai feel. Also, there are many boutique hotels. In CM there are many good ones. You can book them through Agoda or Asiatravel.com.

From BKK give yourself 3-4 hrs to go to the airport and check-in in time.