Walking through the southern end of BeiHai park on our way to a lunch at FangShan restaurant, I was able to get only a glimpse of the park's beauty: the lake, the White Dagobah and the Painted Walkway. Other treasures, such as the Dragon Screen, Five Dragon Pavillion or the gardens the Empress Cixi loved, were not on the way. Given our limited time, we missed seeing these gems. However, the part of the park we did see was truly lovely. It seemed to me immactulately clean, and the gardens we could glimpse walking through the park were exquisite.
The White Dagoba can be seen reigning over the large lake that is the focal point of BeiHai (which means North Sea). The Dagobah was built in the 16th century to celebrate a visit to Beijing by the Dalai Lama. It has been destroyed by earthquakes twice since its original construction; the current version was built in the mid-1700s. The island on which the Dagobah stands is man made, using the earth removed when the lake was dug.
If you have the time, you can rent a boat and paddle about on the large lake (which takes up about 35 hectares or about 100 or so acres). A barge links the island near Fangshan with the Five Dragon Pavillion on the far side of the lake. Swimming in the lake is not permitted, but I understand that ice skating is popular in the winter when the lake freezes over.
Following this link will take you to a detailed description of the sights in BeiHai that I missed.
If your tour includes FangShan restaurant, try to budget some extra time to walk through the park. If you are not on a tour or if you have more than just a few days in Beijing, I think a visit to the park would be very worthwhile. If you are pressed for time, however, you might do better to pass on BeiHai in favor of other "key" sights, such as the Summer Palace or the Great Wall.