The Griffith Observatory is an amazing point where you can see all of Los Angeles. It has a beautiful network of hikes and some that are even covered by Shade. Not a lot of hikes in LA area are covered with a lot of trees, but Griffith Park is vast.
Funny story - that it was getting dark and a small group hiking up the hill. Turns out they got lost and parked at the top. After telling them they wouldn't make it to the top in time I just ended up driving them to the top. YAYA I know... don't pick up hitchhikers blah blah blah, I don't care I only meant well.
What were we talking about again? Oh yeah! Griffith Observatory... A Cool fact of who Griffith J Griffith is that back in 1935 when he passed a way, he stated in his will that admission always be free to the Observatory. It was his land that he donated for Astrology which is a generosity unheard of anymore. Here you can use the telescopes, see the city in it's entirety, hike, and watch live shows.
Many movies and TV shows have used The Griffith Observatory as a film location. I think this place holds dear to me because growing up I loved the movie Rocketeer so much (what young growing boy didn't want to fly?!). I think that was when I had my first crush on Jennifer Connelly. What.... A ... BETTY!!
**** UPDATE **** - Yup... still have a crush on Jennifer Connelly
For more info here's the wiki