Los Angeles Trip in end May

You can visit:

Santa Monica - The Pier (they have a ferris wheel, you've seen this place tons of times in movie. But it's a rather run down small place.) Nearby is the Downtown Third Street Promenade, a street closed off to pedestrians. You will see street performers there, especially at nights.

Beverly Hills - Rodeo Drive is where all the name brands are.

Hollywood Walk of Fame - must do for any tourist - find the hand prints of your favorite film stars and take a picture with your hand on it...

Hollywood Sign - You have seen a million times on TVs, movies and postcards. Those nine 50-foot-tall white letters perched high up in the Hollywood hills. You can get a good picture of it from Sunset Boulevard at Gower and also at Bronson.

Universal City: Its main attraction are Universal Studios theme park and the City Walk. Universal City Walk features restaurants, a movie complex and dozens of specialty shops.

Farmers Market - It's not great as farmers markets go, but nearby there are people giving out tickets for you to be an audience at the TV shows.
http://www.farmersmarketla.com/

Disneyland

Chinatown, Koreatown and Japantown - Well they are considered tourist destinations though of course you may not be interested...

Getty Museum - considered by most as a must see. From outstanding architecture to its collection.
www.getty.edu

Page Museum at the La Brea Tar Pits
You may find it hard to believe but LA does boost some archeaological digs... Natural history museum
http://www.tarpits.org/

Venice Beach - a famous Californian beach!

Marina del Rey: There are many attractions for visitors, including boat rentals, fishing trips, dinner dance cruises, harbor tours and Sunday champagne brunch cruises. Many restaurants are located on the marina's Waterfront Walk, and have fantastic water views.
http://www.visitmarina.com/

A little bit of a drive away from LA - about an hour or two, but some favorite, lesser known favorites you may want to consider:

Solvang was settled by Danish immigrants and the area has been lovingly restored to look like a Danish village, complete with Danish food and crafts. You can take a day trip there: http://travel2.nytimes.com/2006/06/04/travel/04journeys.html

Temacula - Wine country just an hour's drive away from LA. It;s not as famous as Napa Valley, which means it's less crowded, and wine tasting less expensive.
http://www.californiaweekend.com/california-vacation/temecula.html
http://www.roadandtravel.com/travel%20directory/California/ravereviews/temeculavalley.htm

Oh LA downtown is rather unsafe at night so be careful! Have a nice trip!