Hello,
If you are even a little bit of a fan of Museums, I recommend allowing a couple of days for the Smithsonian Museums. They are quite large and there's many of them. You won't be able to see everything, so pick a couple that interest you the most. My favorites are the Air & Space and the Natural History. I've been to each well over a dozen times and I never tire of them!
www.usatourist.com/english/places/dc/smithsonian.html
Of course you have to see the top sights in LA: The Walk of Fame, the Hollywood Sign, LaBrea Tar Pits, Mann's Chinese Theatre. I wouldn't consider them the most exciting attractions. But every city has the "must see" attractions that everyone will ask if you saw. 
Venice Beach can be an interesting stop. Though it's not the best beach for enjoying the surf and sand, it does have an interesting culture. This is where you can find the body builders working out on the beach. There are bikini-clad roller bladers and eclectic artists. And there are a lot of kitchy tourist shops where you can find a cheap souvenier.
A lot of the studios will offer tours. So if you are a bit star struck you can sign up for one of those or possibly get tickets to be a part of a studio audience for one of our TV shows.
If you enjoy amusement parks, LA has a lot to offer. Disneyland, Universal Studios, Knox Berry Farms and Six Flags all have parks in the LA area.
www.usatourist.com/english/destinations/california/losangeles/losangeles-attractions.html
With 4 days you can easily take a day trip down to San Diego. It's about 2-3 hours drive, depending upon the traffic. San Diego is a much more attractive city than LA, with it's mission style architechure. The San Diego zoo is world famous and would be on the top of my must see list.
www.usatourist.com/english/destinations/california/sandiego/sandiego-main.html
LA to San Francisco would be a full day of driving, each way. With the time you have, driving up would be difficult. However you can get a flight for about $100 per person. I just checked our Airline Reservation page for flights in mid-June and found one for $103. You may find that some of the discount carriers offer flights for even less or will be running a special sale. Beware that the prices you see will likely be for each way.
You can check prices for the major carriers on our Airline Reservation page at www.usatourist.com/english/reservations/Reservations-Flights.html
And you can check Southwest, one of the discout carriers at southwestvacations.com
.