If you feel like taking a walk, you may want to consider a walking tour offered by the Los Angeles Conservancy.
"The Los Angeles Conservancy, the largest membership-based local historic preservation organization in the country, is dedicated to the recognition, preservation, and revitalization of the architectural and cultural heritage of greater Los Angeles."
The Conservancy offers a myriad of walking tours (usually on Saturdays and Sundays) at roughly $10 per person. I've only taken one tour, The Broadway Historic Theater District tour, but I loved it. Just be sure to wear your walking shoes and bring your camera and some water with you.
Other tours include: Angelino Heights, Biltmore Hotel, Art Deco, Downtown Renaissance, Evolving Skyline, Historic Core, Union Station and Union Station Family.
For more information, visit, http://www.laconservancy.org/tours/tours_main.php4#about