Family during the day: 3rd street in Santa Monica (great shopping, can walk down to the pier, go to the mall or catch a movie if you want a break). You might want to catch lunch at 'Ye Ole King's Head (a Pub with the BEST fish & chips outside England) (also a great night spot). You can drive up PCH and check out Pepperdine (and meet some great A Phis), stop at Neptune's Net (the coolest biker bar with fresh seafood right on the water up by LA/Ventura County line -- there are a lot of families there during the day & trust me, the steamed shrimp, french fries and beer cannot be beat). From Neptune's Net you can go a few miles up the road to Camarillo and do some outlet shopping or keep driving and head up to Santa Barbara.
A few more places to visit: The Getty Center, the Aquarium of the Pacific, the new Disney Concert Hall (if you are lucky enough to get tix), check out the UCLA Live! Website if you are interested in theatre and concerts on campus while you are here. There is usually a lot going on.
21+ at night: the newest "hot" club is Cinch. I haven't been yet but it is the "in" thing. Another Amy didn't mention is the Standard downtown (really cool bar on the top floor of the hotel).
A few you might enjoy that are less "scene like" are Finn McCools (a Pub in Santa Monica), Tiki Ti (a Tiki bar in Silverlake), Lava Lounge (a Tiki bar in Hollywood), Father's Office (micro brew house in Santa Monica), Dublin's Irish Pub (on Sunset strip), or Saddle Ranch Chop House (very touristy but fun -- you can ride the bull and make smores).
In the Redondo/Hermosa/Manhattan Beach areas there are a ton of fun night spots for you and your friends. You'll love the pier -- you can visit Sharkey's, Hennesey's and many more and there are tons of UCLA, USC and LMU recent grads and seniors everywhere.
If you want to go out in Westwood I would hit the usual suspects: Maloney's on Campus, the Westwood Brewing Company or for something more upscale Palamino (best martinis in town). For Brentwood I'd check out Q's (great pool tables and fun crowd).
If you let me know what part of town you're interested in visiting I can give you more information about your choices. You can PM or email me. You should also check out
citysearch best of LA.
Regarding moving to LA, what do you want to know about living here? I am sure Amy and I can provide you with lots of scoop.
Good luck!