I'm a native Angeleno. Some places to check out that I've found interesting and worth shooting include Downtown-Broadway is a good starting point. If you wander around there is a lot to be seen, Chinatown can be a hit or miss, Los Feliz is fun. The Santa Monica Pier has been good to me in the past, try it out.

Never been to Old Pasadena enough to give a verdict, but have heard positive things about it.

Can't think of anything else at the moment L.A. is surprisingly bland sometimes.