I lived in LA for almost 5 years. My perfect day ...
Go down to Hermosa Beach and hang. Manhattan Beach is nice too, but Hermosa Beach is a little more laid back, not as many snobs. There are some neat little cafes down along Hermosa Avenue. My favorite wsa on the corner of Hermosa and 21st, I think. I know Hermosa Ave is right, but unsure about the cross street being 21st. Anyway, a green building is across from it which houses a C-store owned by Koreans. This restaurant--forget the name, serves great breakfast, so go early, take an outdoor table, and eat while looking toward the beach. Not the best view--you need to walk 20 yards and then stroll south on The Strand for that. The little section of Pier Avenue--about a mile south of this restaurant--that runs between Hermosa Avenue and The Strand is awesome, restricted to walking traffic only, with some cool bars. Sadly, Sharkee's was burned down last time I was there. I watched many a K-State game there back during the DoD.
If you're going to be checking out the stars on Hollywood Blvd, head to the corner of Hollywood and Highland and then drive around the area looking for parking on one of the side streets. If you park in a garage under the Hollywood and Highland Mall you will pay, but there is a parking garage that has an entrance on Orange just about 20 yards north of Hollywood Blvd, and its rates are not too bad. You should spend a couple of hours in Hollywood/Highland area. Go check out the historic Roosevelt Hotel right across from the Chinese Theater. Browse in the Hollywood and Highland shopping mall with the big outdoor quad modeled after D. W. Griffith's set he built for Intolerance, one of the most expensive silent films ever made. You can enter the mall through the Kodak Theater, walking up the steps toward the arena where the Oscars are held. If you get a chance, wander over to the Egyptian Theater (half a block east of the Hollywood/Highland intersection, I think, and on the south side of the street) and see what is playing. They have a lot of cool retrospects there, like a James Bond retrospect or a Clint Eastwood retrospect. You can get a double feature of some classic movies for a good price if you catch the Egyptian at the right time (I went to a Pasolini retrospect and got to laugh at people running from the theater retching).
After that, head over to Los Feliz and follow the signs to Griffith Park Observatory. It's a pretty cool place, great view of the city. The opening of Terminator was filmed there (when Ahhnold comes up naked and works over those three punk rockers), and in Transformers, the Autobots regroup up there before planning their strategy against the Decepticons.
For night life, there are many great restaurants and bars. I like the House of Blues on Sunset because it's the one Dan Ackroyd and Jim Belushi built as a start-up to the franchise, and they get great acts. I went there once and saw The Romantics opening for Jim Belushi's Sacred Hearts Band (and that band kicks ass, I tell you). One of my friends went there to see some local hot band, and Tenacious D showed up as a surprise and performed a couple of sets. This particular House of Blues is cool because if you get a res and eat there before the concert, you get to see how the walls of the dining area open up to transform the place into a concert hall. Great fun.
Another favorite place of mine is Old Tony's down on the Redondo Pier south of Hermosa Beach. There is a bar above Old Tony's that is referred by the locals as the crow's nest, and it is circular with windows 360 degrees so you can enjoy drinks and watch a fabulous view of the sun setting on the ocean. Not to be missed, in my opinion. The restaurant below is a bit expensive, but it has some of the best seafood in the area.
Too bad it isn't football season. Otherwise, I'd reccommend going to Grunions on PCH in Manhattan Beach to watch football. The 10 a.m. game (Pacific Time) was always packed because Grunions televised every game, and fantasy footballers would hang out there getting a start on their drinking, then having lunch, and by the time the early games were over around 1:00 p.m. they still had plenty of time to go to the beach. I actually hated it when my Eagles played the second game--it cut into my beach time. Anyway, not much going on there now. I did watch some great KSU games there in 2000, as well as some not so great ones (great--NU; not so great--OU).
Hope that helps.