What are some of the things you'd like to see in Los Angeles? We have several nice museums, there is the
Grove/Farmers Market that you might enjoy visiting with Rodeo Drive nearby if you'd like to drive through it, as well as LACMA and La Brea Tar Pits,
Warner Bros studios for a tour, and some nice places to eat in Burbank (you can visit the oldest Bob's Big Boy left).
Huntington Library is great to visit, and your mom might enjoy that. Santa Monica is a fun visit, too, and Route 66 ends there, but it's very touristy, and there are those street entertainers that will be asking for money. Newport Beach or Huntington Beach are better to visit (as well as Redondo Beach, but that is probably more out of the way). Santa Monica is at the end of the 10 freeway, and traffic can get pretty busy just getting out of Santa Monica (another thing to keep in mind). There are a lot of nice things in LA, you probably just need to research, and choose your top picks, then go from there.