The inner grounds of the palace are generally not open to the public. Only on January 2 (New Year's Greeting) and December 23 (Emperor's Birthday), visitors are able to enter the inner palace grounds and see the members of the Imperial Family, who make several public appearances on a balcony.
Furthermore, guided tours of the palace grounds are offered during the rest of the year, although no buildings are entered. The tours are held in Japanese, and an English pamphlet and audio guide are provided. The tours must be reserved in advance through the Imperial Household Agency (see links below).
The Imperial Palace East Gardens are open to the public throughout the year except on Mondays, Fridays and special occasions. More information is available on the East Gardens page.