Getty Museum is an outstanding idea. (
http://www.getty.edu/museum/) There are two Getty Museums in LA, the Getty Center (which is the one you want to go to), and the Getty Villa in Malibu (which is nice, but would be way out of your way). I'm not a big fan of the collection there, but the grounds and building, and the views of the city from there, are amazing. Best of all, its FREE! To get there, you would need to catch a bus north on Sepulveda Blvd and it makes a stop at Getty Center, where you can make an easy walk to the peoplemover that takes you to the mountain top perch that the complex is located on.
For entertainment options, LA has some outstanding live music venues. If you are into Jazz and Blues, the Catalina Jazz Club in Hollywood (
http://www.catalinajazzclub.com) on Sunset is one of my favorites. It's not a bar-type club, but rather its a dinner club where you are seated for the show, and they ALWAYS book outstanding talent. It's also a dinner club, but the dinner there is a bit pricey... you don't have to have dinner there, it is possible to just go there for drinks and to see the show. I recommend calling ahead to reserve seats, or having your hotel concierge do so.
Another fave music venue, if you are into jazz/blues, is Harvelles in Santa Monica. (
http://www.harvelles.com) It's on 4th street, just one block away from the 3rd street promenade, and it's more of a typical bar-type live music scene. One of my favorite restaurants in the city is in Santa Monica, The Wilshire (wilshirerestaurant.com), on Wilshire. On some nights (maybe just weekends... but, maybe they do it every night?) at about 9pm or so the place starts transforming from a restaurant to a lounge, usually with a DJ or sometimes live music. Make reservations for a table in the patio, which has great ambience and is a great place to suck up a few drinks and peoplewatch. If you don't like the music or the scene there then no problem!... right next door is another OUTSTANDING live music club called Angels (angelssantamonica.com) which schedules a variety of different kinds of musicians, and best of all there is NO cover charge, and the bartenders pour stiff drinks!