Since you will have a car, you do not need to take a tour.
The La Brea Tar Pits are not very far from your hotel (Wilshire Blvd., just east of Fairfax Ave.). After visiting the Tar Pits, if interested, you can also visit the L.A. County Museum of Art (next door) or the Petersen Automotive Museum (corner of Wilshire and Fairfax).
Then drive north on Highland to the Hollywood and Highland Center (northwest corner of Hollywood Blvd. and Highland Ave.) and park in its underground lot. Come up the escalator and once you walk out to the sidewalk you will be on the Hollywood Walk of Fame. Walk 100 feet to the west, and you'll be at the Grauman's Chinese Theatre. Across the street is (Disney's) El Capitan Theatre and Disney's Soda Fountain. There you will find Winnie the Pooh's star, and, I believe, other Disney characters or notables.
I haven't been on a movie stars home tour, but I've seen agents selling tours in front of Grauman's and also across the street.
TIP: In 1998, we had houseguests from England who were just dying to go on a stars home tour. My DW said she had no interest in the tour, but agreed to take them to Grauman's where they could catch a tour (DW would go shopping then meet them later). Our guests "surprised" DW by buying her a tour ticket. They all went on the tour, and after ten minutes, they all agreed it was the biggest waste of time and money.
Woody