Ideas for my trip in Beijing

Hi guys!
I am a 40 year old norwegian lady going on my first trip to China in may (16-28 may). I am searching the internet for interesting things to do and see, that can take me a bit away from the mainstream/crowded tourism.
So far I am considering 4 nights in BJ, where I of course will visit some of the must sees. But I am also going to take a cookery class in one of the hutongs, and do some proper food eating. Not interested in highclass or tourist traps. Then I am considering travelling by bus up to Huanghuacheng to spend a couple of nights at a recommended B&B there, and do some hiking on the wall and in the surronding area.
Then I am looking at travelling down to Cuandixia, staying a couple of nights there and in Baiyu. Hiking, and enjoying the area after the daytrippers are gone.
Before going back to BJ the last days. Does anyone have better ideas, or tips? It will be greatly apprechiated!
Hege:)