Beihai Park is behind the Palace Museum, approximately one mile west of the rear exit. It is also south of the Houhai area. I saw some tour group go here after the tour in the Palace Museum.
The cost to get in the park is 5 rmb. If you want to go to the temple at the top and the city wall is 15 rmb. The lake is frozen now so is very clam and quiet. There are many lotus plants on the lake. It must be very beautiful during the early summer when they are in full bloom