Check my listing guidebook. https://www.airbnb.com/rooms/3506410 but here are some suggestions that aren't the usual tourist magnets.
Take a day trip to one of the Channel Islands; visit one or all of these iconic examples of Los Angeles residential architecture: the Stahl House; the Frank Lloyd Wright Hollyhock House; the Schindler House; the Eames House; hike the Backbone Trail in the Santa Monica Mountains; climb up the Santa Monica stairs to Adelaide Drive, the most beautiful street in Santa Monica, and view the house Frank Gehry is building for himself--maybe it will be completed by then. Take the Expo line from Santa Monica to DTLA, visit the Broad Museum, the Public Library (don't laugh, it has some incredible art, sculpture etc), visit the Bradbury Building (it had a starring role in Blade Runner and many other movies), take a tour of Disney Hall, eat lunch at the Grand Central Market, Check out the UCLA Sculpture Garden, jog or walk through Palisades Park at sunset. Take a Hollywood sign selfie (search " Take the ultimate Hollywood sign selfie on this Griffith Park hike" for directions). While you are at it, visit the Griffith Park Observatory and pretend you are James Dean for a moment. Catch a drag show at the Abbey in West Hollywood. Visit the Watts Towers and eat at LocoL. Stop by the Blue Whale Bar in Little Tokyo for some jazz and cocktails....
Feel free to message me if you want specific suggestions tailored to your interests.