Okay, let's start with some of the basics:
Things to see and do in Los Angeles:
(1) the beach--particularly either Santa Monica area (my suggestion) or else Huntington Beach or Newport Beach
(2) amusement parks--most well-known are Disneyland and Universal Studios. Disneyland is in Anaheim near the Huntington Beach/Newport Beach area and the other is in north Hollywood, not too terribly far from Santa Monica as long as you have a car.
(3) Hollywood Boulevard--kind of quirky--but overrated in my view
(4) Beverly Hills and the stars' homes (and the TV studios are nearby--so you can go see a show being filmed for free)
(5) Huntington Library and Gardens in San Marino (the place I would go)
and (6) Getty Museum (just east of Santa Monica)
Try to stay out of downtown (a waste with the exception of Olvera Street just across from the train station--which is interesting).
Then, there is the question of going to San Diego. This would be good if you have the time--but it will take you about a 3-hour drive each way from LA--and that is if there is no traffic. Just double this time if there is traffic.
Along the coast:
I'd pick two stops on the way to LA from SF if I were you. Two towns that are a ways apart (Monterey and Santa Barbara) are wonderful places to stop, especially if you also swing by Carmel and drive the 17 mile drive while in Monterey. If you take the single stop instead, you should stop at either Cambria if you take the long drive down the coast route (Highway 1), or else go to either Pismo Beach or San Luis Obispo (a nice college town) if you go directly down Highway 101. Another option many people like is Paso Robles since it has lots of wonderful wineries in the area and is reasonably priced (unlike the overpriced Napa Valley/Sonoma area wineries).
Also, make sure you stop by in Solvang--an old Danish town (just north of Santa Barbara on the inland side) before going on to spend the night in Santa Barbara. Michael Jackson's Neverland Ranch is near here, as is Ronald Reagan's old ranch.
In Monterey, the things to see are the Monterey Aquarium, Cannery Row (right next to the aquarium), the coastline just south of here (which leads to the 17 mile drive), the Pebble Beach area and the city of Carmel itself. Near the downtown area is the Fisherman's Wharf--although there's not much to see downtown, so I wouldn't spend much time there.
In Santa Barbara, the things to see are the Mission (the largest one in the state--and the most well preserved)--(P.S. there is also a mission in Carmel, near Monterey, as well as 20+ other ones up and down the coast)--but I digress, so let me get back to discussing Santa Barbara. You should go see the beach and if it's a weekend it, they will have arts and crafts festivals down there. Go up and down State Street for a lot of fun and good shopping.
For Las Vegas, I'll let others answer--like vegasmike6 or Ham Radio. I was just in Las Vegas two weeks ago--but the town is changing so much and I was there for such a short time that it is hard to comment on the best places to see or stay. I personally like Mandalay Bay, but since 15 of the 20 largest hotels in the world are in Las Vegas--the choices are pretty much endless--and where you go depends upon your budget and whether you are there in the middle of the week or the weekend--and whether you are going in the summer or winter.
Enjoy
