Angels Stadium and Honda Center (Anaheim Ducks NHL hockey) are about 4 miles away. Dodger Stadium and Staples Center (Lakers and Clippers bball, Kings hockey) are about 35 miles away. If you like college sports there's plenty of that - USC, UCLA, etc.
What else? Beaches, mountains, deserts, TV tapings (Leno, Kimmel, numerous sitcoms), movie studio tours, Griffith Park Observatory, Hollywood Bowl, etc etc. There's a parade in Padadena on Jan 1st. Are we getting warm?