I visit Beijing with a friend from England. Below is what he think. I think this is a good thing to listen what a foreigner may think of Beijing.
Yonghegong Lama Temple- -This is one of the few operable temples in China. It is smaller than the Forbidden City and Temple of Heaven, but is worth examining. There are 60 monks of the Tibetan Lama order residing in and maintaining the temple. Across the street from the Temple are a few Buddhist shops. However, a bit further down the little alley on the left is an artist shop with intriguing sculpture. Yonghegong is north of Ciao Ciao Gelato so I recommend a few scoops after enjoying this place.
Great Wall (“Chang Cheng”)- -Unfortunately, one needs to drive all the way to Simatai or Jinshanling (3-4hours) to get away from the crowds at the Great Wall. However, most people choose between Badaling or Mutianyu. I recommend Mutianyu since there are still parts where one can trek off the beaten path. There is a cable car at Mutianyu for those that cannot brave the half hour step climb to get to the wall (never mind the climbing that will be incurred once atop the wall). When you get on the wall, go right...this leads to the fun parts off the beaten path (this is beyond the restaurant one passes along the way). Badaling is a closer drive to the Wall than Mutianyu, especially with the new Badaling expressway opened. However, Badaling is swarming with tourists and cheeziness. I guess if you have major time constraints, do Badaling, but, if possible, do Mutianyu instead.