Griffith park is one of the largest parks in Los Angeles there are endless activities to find if you explore the area. There is horse back riding, and lessons. There is also an old carousel, and an old camp from the early 1930's.
If you are the adventurous type there are an array of trails that lead all throughout the park and to the old zoo, and the new zoo, and a couple of museums. This also includes the observatory, the Greek theater, and travel town.
Mon-Su: Open 24 hours