There is a great deal to do around the Forbidden City because the Forbidden City is the central focal point of the entire planned city of Beijing. The city branches out from the Forbidden Palace and has several ring roads circling the central Palace area. South of the Forbidden City you'll find Tiananmen Square, which is famous enough and worth seeing (you can't avoid seeing it as you enter the Palace).
Further south you'll find Qianmen Market Street, where you can buy souvenirs and do a bit of shopping after seeing the Palace. This is a great, cheap place to find tea, trinkets, T-shirts and more.
Also to the south you'll find teh hutong street of Liulichang, a culture street selling art and musical instruments. This is a pleasant enough walking street as well.
To the north of the palace you'll find the Drum and Bell Towers, Houhai Lake, and Nanluoguxiang. The lake is perfect in the late evening and the nightlife around the lake is impressive. The Drum and Bell Towers lie in the heart of one of Beijing's oldest Hutong communities and is amazingly popular for rickshaw rides. This whole area is well worth a visit and lies north of Jingshan Park, or coal mountain as it is called in English. This park is one of the best views of Beijing as it is centrally located and looks out over the Forbidden City's orange rooftops.
North of Tiananmen Square
Dong Cheng District
China's greatest imperial palace complex...
Forbidden City, Dongcheng, Beijing
A wealth of information on the Forbidden City and More...
Chang An Avenue
Dong Cheng District
Geographical and symbolic center of Beijing...
Qianmen Dajie
A recreation of an ancient shopping street...
Yan Dai Xie Jie
A beautiful and romantic lake circled in classy bars and restaurants...
Runs north to south between Jiugulou Dajie and Dianmen Dajie, respectively
Southern entrance a few blocks east of Houhai
Hutong chic, for shopping, cafes and adorable bars...
44号 景山西街
Bets views of the Forbidden City...
Sou Xin Hua Street, Xuan Wu District
Cultural artifacts on ancient shopping street...
Di'anmen Dajie
Enormous Bell...
Di'anmen Dajie
Listen for the Time...