We live just below Griffith Park and the Observatory is one of LA's most amazing places. They say it's the best place to get a good view of the Hollywood sign. It's featured in countless shows and movies, mostly recently, LaLaLand. It's about an hour hike from the bottom of the hill and overlooks the entire city. It's free to walk around and if you're lucky the telescopes will be open to the public. It's gorgeous any time of day.
LACMA is one of our favorite museums in LA. It has a great collection of Persian art, (for those that don't know, Roxy is Persian), a wonderful permanent collection, great temporary exhibits, free jazz, and special screenings. You've probably also seen those famous streetlamps in shows and movies. Safe to assume that everything in LA you've seen at one point in a movie or show.