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.
Authentic Korean BBQ in Koreatown. Delicious meats and big variety of mushrooms, interestingly good fried rice, metal chopsticks, and a buzzer you can press to alert the waiter.
Right by my apartment, I can't help but come here often. It's situated right around the historic La Brea Tar Pits. One needs to spend an entire day here. Also love their magazine/book store.