Well, fun is just going into Hollywood or Melrose to get some shots of people and places. There are interesting buildings, shops, people and tourists. Most shops won't let you shoot, and most people are pretty camera-grumpy as well, so it teaches you to deal with them. "If you can make it there, you can make it anywhere!" Another place is Venice Beach. Surprisingly lame are 3rd Street in SM, and Pasadena's Colorado Blvd. Downtown, on the other hand, can be actually dangerous if you're a Valley kid without a lot of street experience. (No disrespect intended.)
One thing you can do is get on Sepulveda, and just drive South on it from the Valley. There are so many cool places, you could fill a week of shooting. One of my all-time favorite weird locations is the Sepulveda Dam. Another place is the Veterans Cemetary between Sunset Blvd and Santa Monica Bld. You pay $8 (or something like that) for a permit, and promise not to shoot people's names, and not to use the images in negative context, but it is a great place to shoot. You go through Culver City (pretty) past the airport on to Inglewood and El Segundo. You can go all the way to the South Bay and Palos Verdes, past the Harbor, and at some point you end up in Long Beach.
The Getty is pretty cool. They let you shoot, and there are some interesting gardens. I also like the Farmer's Market on Fairfax (and the rest of Fairfax) as well as the Sunday market in Hollywood, on Ivar near Vine. It's between Hollywood Blvd. and Sunset.
I've also had lot's of fun shooting the Sunset Strip on a Thursday night when all the bands are playing the Roxy, the Whiskey, the Rainbow Room, or down by the Troubadour. They're not going to let you shoot inside, but the sidewalk is free game. Just tell 'em you're a rock'n'roll blogger and give 'em your website, all those people want to be famous and will strike any pose you ask. Don't be shy.
Do a project: shoot people worshipping. Every religion known (and some just developing) worships in LA.
Check listings for odd swap meets, car shows, fairs, dog competitions, marching bands, God knows.... it's one of the greatest cities in the World in the history of mankind, there's a LOT to shoot. Just get away from the computer you're sitting in front of.
Can you tell I love LA?