Of the Confucius Temple, Confucius Mansion, and Confucius Cemetery, the Confucius Temple is my favorite. You can experience the reverence shown to Confucius by successive emperors and visit the old well at the Confucius Residence. The Confucius Mansion is the residence of Confucius' descendants, and the Confucius Cemetery is the burial site of the Kong family. You can purchase a combined ticket for both.
The Confucius Temple also features performances including the opening and closing ceremonies, a Confucius memorial performance, and a light show. Staying near the Confucius Temple is highly recommended for convenient viewing.