Wow, where do i start?
the Farmers Market at Third and Fairfax a Los Angeles landmark - it is a permanent installation, very big, and has lots of food vendors. It is a great place for lunch. It is also right next to The Grove which is an awesome shopping center (like a Barneys outlet...)
another good one is the Los Angeles Museum of Contemporary Art (MOCA), which is a superb and very large museum of all things modern art. You can easily spend half day just there, and it is next to a very interesting park where they found mammoth fossils.
the planetarium on top of Griffith park is also very interesting, and there is an awesome laser show in some nights. The park itself, Griffith Park, has nice hiking trails.
A great drive is Mulholland Drive, is is a winding drive that offers views of hollywood, LA Basin, the Hollywood sign, and multimillion dollar houses. You can even enter the gated community of Bel Air, if you really want to see where billionaires live.
If you feel like walking around, Venice Beach is the best beach for people watching
if you feel like a Midrachov, Santa Monica has a great no-cars-allowed street with tons of vendors and food
Last by not least, a great LA visit should drive on pacific highway to Malibu, where you can hang out at the famous beach, eat in a seaside restaurant, and see all the stars' villas.
ENJOY!!