The Summer Palace
Extensive gardens and the ruins of palaces constructed by the Qing emperors. In 1860, foreign soldiers damaged much of what was then known as the "Garden of Clear Ripples", but the area would be rebuilt and renamed by the Empress Dowager Cixi, using funds intended for modernizing the Qing navy. Most visitors stay in the front hill area, but if you prefer quiet places, the west bank and back hill areas are good choices. There are some quiet and secret ruins, caves, and other fun stuff in the back hill area. You could easily take bus No. 690 or 808 from Tian'anmen Square to the terminal station, the Summer Palace. The Bus 826 would bring you from Temple of Heaven to Summer Palace. Also, you can take the subway line 4 to Xiyuan station, from there it's a 10 minute walk.
The Old Summer Palace
Built in the 18th and early 19th centuries, these gardens were home to the emperors and Qing court. After their 1860 destruction by British and French troops the gardens was not restored, and the ruins that can be seen today still serve as a reminder of the costs of imperialism. Bus 690 from Tian'anmen will also get you here.