It's a cemetery, but the view from up here is stunning and you can see one of the most large scale epic paintings ever made by a human: The Crucifixion painting, by Polish artist Jan Styka. It's a must see.
Home State is known for their Texas-style breakfast Tacos. Next door to it there's a wine bar called Bar Covell, which lets you bring your tacos from next door and eat them while you have a glass of wine. Don't order more than two breakfast tacos if you don't want leave there with your pants unbuttoned.
This is the place you want to go to have a awesome brunch. Be prepared for a waiting line outside on the weekends. The place is packed then. My personal favorites is the Polenta with Maple syrup, bacon, spinach and chicken apple sausage. If you had a rough night before I would suggest the "Hangover Helper", with the bottomless fresh mint-lemonade. Always does the trick.
The Day of Death is one of the most amazing experience you can get from a city like LA. Every year, during the week-end of Halloween, the Hollywood Cemetery becames the stage of the most candid and beautiful celebration of life and death I ever seen.