Hollywood is always a fun place to visit. I use to work there too. You can run into lots of filming and celebrity. I go there to tour the celebrity museums and the film studios. I also love the downtown shopping center in LA. It has everything that you're looking for.
Hollywood blvd or Sunset blvd. has great shops and museum on the strips. You can do alot of shopping plus eat really good too. You have to pay for parking space though. This is the worst part. There's no free parking in LA. This is very irritating. You can't stay for long. You can only be there for a short time because after that the meter start going up. This is what I don't like about LA.
Hollywood has the Kodak theater and the Chinese man theater as the site for tourists. They can take a great deal of photos here. They can see all the hands and foot prints of all the famous actors.