As of right now I am going by myself to check the sights out before I leave with a group to Vietnam (Missions Trip). Now I looked at Hotel Prices and they are around 200 a night by LAX. There are hostels that cost $20, anyone opt in for a hostel? Never stayed at one. Also, what is some cool loner things to do in California? WhaleWatching, Universal, and Alcatraz seems cool. Wouldn't mind surfing either.
Hmm... it depends on a few factors (when exactly you'll be there, how much money you want to spend, what sorts of things you're interested in, etc.). One of the most beautiful places to go for a concert in the world is the Hollywood Bowl. In May this year they have LCD Soundsystem and Paul Simon, among some others. You can check out their calendar here. Local theater is wild in Los Angeles (especially in Hollywood and North Hollywood), due to all of the actors and actresses and other talented people. If you have an opportunity, and enjoy that sort of thing.
Universal's a fun theme park, but for me Disney is still the king. (I guess it depends in part on whether you've been to a Disney theme park before, etc.) If theme parks are your thing, the lesser known option is Knott's Berry Farm -- but that's a So-Cal classic. If you go, be sure to get the famous chicken dinner (which requires standing in its own line, so plan ahead). Or: there is Medieval Times in the same area, though that's not quite the same thing.
StarOcean mentioned the San Diego Zoo, which is brilliant, but if you don't want to travel that far while you're in Los Angeles, the city has its own zoo in the middle of Griffith Park, which is also home to Travel Town (old train engines, etc., if that kind of thing interests you), the Gene Autry Museum, and the Observatory. Those sorts of things can make for a laid back sort of day, especially if you enjoy park-type activities.
Then there are the beaches and all. Santa Monica has the famous pier, but it's a very crowded, touristy area. Still can be fun. Maybe you can get out to Venice, which is... an interesting place. Or if you want a pure beach experience, there's Malibu. (I dunno anything about surfing, personally, but that's where you can do it.)
Alcatraz is awesome, but that's in San Francisco -- which is far outside of Los Angeles, a six to seven hour drive. I mean, if you want to do trips to SF or San Diego (or Las Vegas), each of those cities has its own sites and activities. But if you want to check out L.A. while you're there, there's plenty to do. I was born and raised in Los Angeles, so let me know if you have any more questions.