Note: I have never been to most of these places. I want to go some time. Enjoy, Drew (and others). LA people, please contribute suggestions!
  1. San Pedro ...
    Apparently you can get a tour of the docks that will blow your mind. @MCWarburton told me this.
  2. Watts Towers ...
    I've been to this one. Spires of colorful garbage (literally) built as an urban art project in a tough part of LA. Take main streets there. Get a tour. It's cool.
  3. Whittier, California ...
    12 miles southeast of Los Angeles. According an article I once read in Los Angeles Magazine it has an uncannily preserved 1950s downtown with a main walkable downtown that sounded cool to explore.
  4. The Magic Castle
  5. Mai Tais at Tikki Ti
    Suggested by @sashabronner
  6. Griffith Observatory
    Suggested by @sashabronner
  7. That bowling alley in Santa Monica, on the left hand side
    Suggested by @sashabronner