Have you visited the Summer Palace? And do you plan teaching English in Beijing? I had hard times with taxis since no driver spoke English. Having a Chinese friend with you was a must (for me at least). Another place to go and have a look at is the street were they sell tea (there are probably many). This one was about a kilometer long and had hundreds of tea shops along side. But there you definately need a Chinese guide.
Has the air quality improved? Back then I couldn't see high rise buildings 5 km away from the Tsinghua University dormitories, and that was in May. Also, spending that one and a half months in Beijing became a drag some times. If I tried to go anywhere from the University Campus, I needed a Chinese friend to tell where to go and which bus to take. I didn't want to bother them all the time. You probably have it differently.