Visiting LA

The Santa Monica Pier and surrounding area is really fun. If you love movies/Hollywood then be sure to check out all the foot/hand prints in front of the Chinese theater (Sunset Blvd, I think?) It's kind of a trashy area but still cool to see all those names :)
Of course you may want to check out Beverly Hills and Rodeo drive.
I have also heard that Catalina is awesome though I've never done it myself.
Have fun!!!

Every State/city, has a tourism website.
Google search it and they have tons of info.

House of Blues for a show?
Rodeo Drive for shopping?
Check out the aquarium/Cannery Row in nearby Carmel?
Go to Venice Beach?
Santa Monica Pier is fun too!

Universal Studios would be fun!

I would start with what is your M. up to, what's her mobility, energy level, crowd tolerance, is money an issue? There really is so much to choose from, but if you factor in the questions above, you'll weed out so many places. My M. for example has energy and mobility limits, so she'd prefer places that she wouldn't do a lot of walking. There is the must see for so many, Disneyland (that's 1,2, 3 days there), there is a huge range on museums; LACMA, MOCA, The Getty (requires reservations), Natural History museum, lots of smaller but good museums too Norton Simon. Then there are landmarks and tourist destinations like Venice boardwalk, Hollywood walk of fame, Chinatown, Beverly Hills Rodeo Dr....I can go on and on. Then there is the actual spending time with your MIL is she willing to do the sightseeing? Have fun!

The aquarium in Santa Monica is awesome!

I live in Southern California and prior to last year at New Years I had not done the tourist things in Los Angeles. My daughter's great friend from Sea World camp came for the holidays so we did it (from Rhode Island, totally wanted to do the Hollywood thing. For LA/Hollywood we did the Santa Monica Pier in the morning and hung out there. We went to Hollywood and parked at Hollywood &Highland, it was ample parking and a big shopping area. From there we were able to walk to the Chinese Theater, the Ripley's Museum, the wax museum, walked around on the Hollywood Walk of fame, saw all the crazy street characters and found a great place to eat. We drove to the Hollywood sign as well (hard to find).

There are also lots of places not right in Hollywood: Getty Museum (reservations required), The Aquarium of the Pacific in Long Beach (Queen Mary is right there), other theme parks (Universal, Disneyland and of course Sea World that would be closer to home). Not sure when she is coming but the boat parade in Newport beach is awesome (I think Dec. 17-21).

I bought the Frommer's Los Angeles book...So many things I didn't mention. They give sample trips for one, two and three days. I would buy it if I were you.

Have fun.