S.R.
LA is so huge it depend how long you will be here, what you like, and where you will be staying. How do you like to spend your days, how much driving you like to do.
I personally like the beaches. Santa Monica and the pier is cool, so is venice beach. Otherwise for beach towns I'd head south to Newport (balboa island) or Laguna. Manhattan beach and Hermosa beach would also convey the LA beach vibe. You could go to malibu and walk the sands up and down for celeb sightings. If the weather is good.
I think Griffith Park is cool, there is the observatory, and hiking trails, and the LA zoo.
The original Farmers Market near 'The grove" shopping center for delicious food, that's two places you can go that are right near each other.
I like Olvera street (it's small) and China Town both within walking distance of each other for all little culture contrast. You could also do something downtown that same day, like go to the Bonaventure hotel. It's beautiful, if you go in the evening you can get drinks at the restaurant/lounge at the top, it rotates around and you will get gorgeous views of LA as the night falls.
If you are into architecture you can check out Disney Concert Hall and the LA cathedral, maybe the Getty Center.
It is also fun to go to the magic castle, but I think you need to be invited, otherwise you can go to Yamashiro's restaurant for dinner and magic.
Feel free to PM i can get more specific if I know what your style is and where you'll be.