I went to the Watts Towers when I was a kid. It is amazing to look at, but I think it is more of a class field trip kind of thing (in my opinion)
It is interesting, but if you have limited time, I would recommend the Getty (either old or new), or LACMA and the Petersen car museum - if you like cars.
Also, if you have a chance, the Santa Monica Pier/Beach can provide a nice afternoon/evening. The Third Street Promenade has some decent restaurants and good people watching if you want to be near the beach. But, it does get pretty crowded, especially once summer hits.
Venice Beach can also be fun.
If you are downtown, LA Live (where the Staples Center and the Convention Center are, along with the Nokia Theater) has restaurants and shops. Parking is pretty expensive, but there is mass transit options.
LA Live is probably 12-14 blocks from the Music Center, which houses the Ahmanson/Market Taper/Dorthy Chandler/Disney Hall. The Dorothy Chandler has LA Opera performances. I believe Tosca is playing during that period.
If you are a baseball fan, Dodger games can be fun, but traffic in and out is a nightmare. As others have said, if you can go to the Hollywood Bowl, that is wonderful. If you go, I would recommend you park in Hollywood and Highland and take the shuttle bus to the Bowl. Stop at Trader Joe's first for some wine, cheese and munchies.
A lot really depends where in LA you are staying. There are plenty of destination stops, but also smaller things to do if you are in a specific neighborhood.
Music Center.