I’m not sure how I managed to miss them, but there is a state park–actually more of a garden–and a winding aerial pathway that wraps all the way around Disney Hall, high above the street level. The garden is charming and the views are spectacular.
The entrance is at 2nd and Grand Avenue where 60 stairs take you up to the garden. Not up for that number of stairs? There is an elevator in the building you can use. There are docent tours, too. Here is some of what I saw on a warm Sunday afternoon.