Yep. You haven’t told us what you like.
It’s a pretty good city for Museums as has been noted above. I’ll second the recommendation for The Getty (Note that there are TWO of them, both worth seeing). LACMA is more than respectable as Art Museums go. A decent “under the radar” art museum is The Hammer Museum. The Peterson Museum isn’t my thing, but if you’re into cars it’s definitely your thing. I disagree with Senegoid that the Reagan Library is worthwhile whether or not you’re a fan- I’d say it is only worthwhile if you are a Reagan fan or, otherwise, a Presidential History buff.
If you’re going to do the Zoo, definitely do The Autry Museum which is right across the parking lot.
If you do the Observatory, enjoy the view as Elmer J. Fudd suggests but also go inside it’s awesome.
Of course, if you’re not into museums disregard all of the above.
Like hiking? One of the things I love about L.A. is that you can spend the day on wonderful hiking trails in the Santa Monica Mountains without leaving “city life” behind. As soon as you return to the bottom of the mountain, you can walk right into a great restaurant or shops (depending on how sweaty you get hiking!).
Music?
Here’s the calendar for the L.A. Music Center. In March, you’ve got “The Flying Dutchman”, John Adams’ “The Gospel According to the Other Mary”, and Wynton Marsalis in concert.
Less “fancy pants” music?
Best places for internal quality control (meaning that generally you can stop in without knowing who is playing and still expect it to be pretty good), I’d suggest Room 5 and The Hotel Cafe.
Want to check out the Whiskey or the Viper Room on The Sunset Strip? I’d say you should first familiarize yourself with the bands on the bill- internal quality control isn’t as good at those places. If the band is good, then yes those are cool places to hear music.
Live Comedy?
You can pretty much expect a decent show any day of the week at The Improv, The Comedy Store, or The Laugh Factory. For atmoshpere, I prefer The Improv of those three. My PRIMARY recommendation for Comedy would be The UCB Theatre (the original is in New York, but there has been a vibrant community growing around the L.A. Theatre for several years now). Click on any show on the calendar for details. The theatre is very nuturing to new talent and encourages risk taking- the shows that lack any “names” are actually most likely to be the coolest shows- so, stop in there for anything. The theatre’s “signature” show is called ASSSSCAT- which is every Saturday and Sunday (the Sunday show is free, but you have to line up ridiculously far in advance to be sure to get in).