Once in Beijing, you should not miss the Great Wall. However, finding a decent tour without 2 million tourists can be a real challenge. Nearest and most accessible part of the wall is Badaling. If you absolutely want to go there, do so on the weekdays. Second to Badaling is Mutianyu, which is a bit greener, a bit farther, but still very touristy. These places offer a cable car as an alternative to climbing a significant amount of stairs. Important to note that most hotels and hostels offer daily tours only to these places.
A refreshing exception is Leo hostel. They do a tour called “ancient wall + secret wall”. This one day tour will take you to a part of the wall, which is actually not much reconstructed. (Frankly, if you go to Badaling, the conditions might raise some questions about the real age of the wall.) You don’t have to stay at the hostel to take the tour, just book it at their reception and show up on the day when the tour is scheduled. The tour will take normally around 20 people, and on the way not only you can see documentaries of the wall, but they air a couple of China-related episodes of South Park just to cheer up the folks before the hike. The actual hike is not the easiest one. The complete hike is to climb up to the 6th tower and back. This means around 1.5 hours climbing up, and 1.5 down. Of course you can turn back any time, out of the 20, only 5 of us made it to the 6th tower. Nevertheless the higher you go, the better panorama you will be offered, and you find parts of the wall that are really overgrown by vegetation.
To read more about the tour, visit: http://www.leohostel.com/LEO_HOSTEL_TOURS.html