I remember a place one hour north of Beijing called "Camping Beijing". Wonderful place with 24h security. You can rent a lot, costed me 195 yuan per night with my Chinese girlfriend and a friend of her.

But be careful when eating those S'Mores, those are succulent but they pack quite those calories!

Beijing actually has lots of camping spots. As Poutine mentioned above, Camping Beijing is a major camping site (http://www.campingbeijing.com/), but other campsites include the forest park at Yunmengshan some 80 km from Beijing (http://www.yunmengshan.net/). Lingshan Mountain and the Green Dragon Gorge are also good options, as are various spots around teh Great Wall. The Miyun Resevoir also has some picturesque spots although I'm not aware of any designated camping sites there. You might have to rough it in the wild. I've also heard of camping sites around Shidu.

You can camp at Jiugukou Natural Scenic Ares  ( 九谷口自然风景区) in Huairou District. It's possible to set up a tent there, have a bbq and take in the serene nature. If you can read Chinese, this article highlights many camping options in the Beijing area: http://www.bjlx.com/BJ_Article/zx051210143734.shtml

I have to say that most scenic spots fit for camping in Beijing don't provide services or guides in English. The only one I heard offering services in English is Beijing Youth Camp International (www.qingnianying.com). They have a team who are experienced in communicating with foreigners. Maybe you can take a try. Good luck! 

4 years 2 years and 3 hours...wtf?