I grew up in Southern California, so I may be jaded in my view of the tourist attractions.
What in Hollywood do you want to see? The Hollywood sign? Some of the grand old theaters, like Grauman's Chinese and the stars on the sidewalk? That will take you about 30 minutes, max. By walk of fame, do you mean the stars on the side walk?
What in Beverly Hills? Rodeo Drive? The movie stars homes (most stars live all over the place, not just in Beverly Hills).
What in downtown LA? And what do you consider downtown LA? I worked in downtown LA and when I was there, there wasn't much to see, and it was an area we were told to clear out of before it got dark.
Are you going to try to see some kind of performance at the Dolby Theater, or just drive by to see it?
I spent many summer days when I was a teenager at Santa Monica beach. Don't remember anything memorable about the pier, but again I may be jade. And sad to say, I've never been to Venice Beach.
Some years back we took a coastal vacation by car with our daughters. We didn't spend more than a night or two anywhere, but we did stay in Beverly Hills (at the Hilton) on the way south. It was a pretty good location to get around. We didn't go most of the places you mentioned but we did go to Rodeo Drive, the LaBrea Tar Pits, and UCLA as our younger dd wanted to see it.
Wow, Luanne, you seem to have totally missed the boat on great things to do in LA. Just in three minutes off the top of my head--
1. Hike or horseback ride in Griffith Park
2. Directors screening of a movie at the Arclight Cinema
3. Studio tour- best bets are Paramount or Warner Brothers
4. Walking food tour or downtown LA, visit Angel's Flight, the Bradbury Building and Grand Central Market, visit the Broad Museum, catch a show at the Disney Concert Hall
5. Universal Studios theme park
6. Walk Venice beach and canals
7. Ride the rides on Santa Monica Pier and visit the incredible Wed or Sat Farmer's Markets
8. Great museums like Getty, the Getty Villa, LACMA, Petersen Automotive Museum and yes, I agree- the LaBrea Tar Pits
9. Eat fabulous food in one of the best food cities in the world
Personally, I'd say look for an AirBnB in the Laurel Canyon area. We used to live there and apart from rush hour, you can zip east-west on Mulholland Dr fairly easily.