Great question. I haven't been to Hawaii yet (on my list!) but have lots of suggestions for LA. The area is so vast that the best spots depends on interest, time, and transport, in that order. A private car is much faster than the public transit network.
Here's my must-see list. Apologies for the length; there's just that much to see.
Movie related sites:
1. The actual Hollywood is now a psudeo-theme park aimed at tourists, but is still fun. See the stars on the Walk of Fame, and the footprints at Mann's Chinese Theater. If it interests you, tip the costumed characters for a photograph.
2. Musso and Frank is the only restaurant remaining from the golden age, and incredibly atmospheric. You have a great chance of spotting a star too. If you go, dress nicely, hide your camera well, and expect a large bill (it was completely worth it, though!)
3. Warner Brothers Studio runs a behind the scenes tour that covers the day to day work of movie making. They have tight security, so reserve as far in advance as possible
4. If TV shows are in production, you can be in the audience for a taping. Most of the tickets are given out by brokers; search for them online.
5. Many companies run entertaining tours of LA that focus on stars' homes and the like. Their accuracy varies considerably; in general the more touts the more fanciful the tour. Finding a good one requires considerable research. Alternatively, pick up the book "The Ultimate Hollywood Tour Book" by William Gorden and create your own star tour.
6. Many stars are buried in Forest Lawn Glendale, the gaudiest of LA's many cemeteries.
Beaches:
7. Venice Beach is LA's alternative beach scene, with lots of street performers and memorable characters. It's also the home of the famous Muscle Beach workout site. The water quality is questionable.
8. Santa Monica Beach is upmarket, and an hour walk from Venice Beach. Great shopping and food, and the water quality is descent.
9. Huntington Beach in Orange County is the focal point of surfing in LA.
History:
10. Downtown LA is a long neglected area that has undergone a huge revival. Los Angles State Historic Park contains the original settlement. Chinatown, Little Tokyo, and hispanic East LA are close by too. The Los Angles Conservancy runs highly recommended walking tours of this area, including one that goes inside golden age movie theaters.
11. LA has many houses designed by leading post-war architects (Frank Lloyd Wright, Richard Neutra, and so forth). Some are open to the public; lists are online.
12. The La Brea Tar Pits starting trapping animals during the Ice Age. No dinosaurs, but lots of wooly mammoths and so forth.
13. The Huntington Library in San Mateo contains one of the largest rare book collections in the United States on public display, plus extensive gardens.
Strange and wonderful:
14. The Museum of Jurassic Technology is a natural history museum as envisioned by a mad scientist. Words can't describe this place; its that weird.
Theme Parks:
15. Six Flags Magic Mountain has the second largest collection of roller coasters in the United States, and ranks at the top in fan polls. To keep the lines manageable, go during the week and arrive before the doors open.
16, For theme park rides, I prefer Universal Hollywood to Disneyland because the tickets are cheaper and the lines shorter. Both are incredibly well done entertainment on a grand scale.
Window Shopping:
17. Unless your budget has at least six figures, shopping on Rodeo Drive is unlikely, but looking is still free. The stores are closed on Sunday.
18. South Coast Plaza is an absolutely huge mall that mere mortals can afford (a few) things in. In some ways, its the ultimate distillation of the LA experience.
.
Reply to this 
