Take subway line 4, get off at Xisi, and you can go shopping and stroll through hutongs. Go straight to the east for about two stops, which are Shichahai, Houhai, Jiumen snack and Soong Ching Ling's former residence in old Beijing.
Get off at the Zoo on Line 4 and go to see the giant pandas.
Get off at the east gate of Peking University on Line 4 and visit Peking University.
Get off at Yuanmingyuan on Line 4 and visit Yuanmingyuan.
Get off at Beigongmen on Line 4 and visit the Summer Palace.
My order is from near to far, you can choose.