I've never done a tour but here are some things I like:
Griffith park observatory (not for the museum but for the views and usually on the way to other stuff I'm doing anyway)
Little Tokyo (especially the mochi ice cream store and sanrio store plus choose a sushi restaurant that pull the food around on little boats or the restaurant where you order on the touch screen and food delivered via tubes)
Canters diner(cool atmosphere, 24 hrs, good Jewish food, cool neighborhood next to Hollywood)
Warner bros studio tour (if you do this one then you should eat at Porto's before/after, good Cuban food and go vintage shopping at the shops on magnolia)
Santa Monica Pier is kinda cool but usually crowded
If you want to go to the beach pick one in Malibu. The water will probably be cold though
I think watching the price is right live is fun and then after you could eat at the original farmers market
FYI I'm from LA and moved away when I was 17 so all the things I know I like to do there is from that teenager perspective lol