Most big cities in China, of sufficient age and with sufficient mind to preserve the old, have a bell tower and a drum tower. Usually, these are in the town square or somewhere nearby. In Beijing, they are located on the city's famous center line (the line denoting the center of the Chinese Empire—the Forbidden City marks the exact center of this line). The bell and drum towers were the town clock of ancient Beijing. The bell tower rang the hours of the day, and the drum tower beat hours of the night (the drum was called the voice of the earth, and the bell was the voice of heaven).
The drum and bell towers are a great start—provided you don't mind climbing about a hundred really steep steps in each tower—to a day in Gulou. Gulou is one of the newly gentrified and increasingly hip areas of Beijing, but it still retains all the charm of an old hutong neighborhood.
The towers are best approached from the Gulou Dajie subway station, on line 10. From there, you can see the towers, walk toward them. The ticket cost is 15 RMB for the Bell tower, 20 RMB for the Drum tower, or you can get a through ticket (covers both) for 30 RMB. In the drum, there is an exhibit of timekeeping in Ancient China and a drum show every two hours.