While you're in Beijing, you must take a day and visit the Great Wall. It's certainly one of the most impressive man-made structures in the world. There are three spots where you can visit the wall: Badaling, Mutianyu, and Simatai. Of these three, Simatai is the best place to visit: the other two sites are horrid, as most tourists go there and it feels like a carnival with tacky souvenir stands and amusement park rides. Although Simatai has a hideous cable car that looks as if it belongs at the Alabama State Fair, it feels like the genuine Wall that we've all read about in our history books.
Simatai is about a three hour bus ride from Beijing. You won't find public transport there, nor would you want to take it anyway. You can look for taxis and buses parked near the KFC in Tiananmen Square. The best bet, however, is to take a tour from the Jinghua Hotel. Their booking office can be reached at 761-2582. When I was there, the manager of the office was a Chinese-American who was very helpful.
Simatai is often treacherous. Make sure you have good walking shoes, and a backpack in which to keep your things, because it's a steep climb! The trick is to keep on walking and walking. Eventually the loud, obnoxious tour groups will turn around, and you will be on your own. Eventually the wall juts up at a 90 degree angle: it's still possible to climb and continue, but not if you're prone to nosebleeds or have a fear of heights.
The food here is hurting, so bring snacks that will tide you over, as well as enough water. You will be followed forever by vendors who will insist that you buy their bottled water or post cards. Simply ignore them and don't feel emotionally blackmailed into buying something. Just continue your walk.
Have a great day. My day spent there was exhilarating.