There's lots of great riding in LA. Often, though, you need to ride through/near heavy traffic to get to the good stuff. Also, your options on the weekend will be a little different than during the week. The major options:
1. (East) ... Angeles National Forest. There are a handful of beautiful roads ... Angeles Crest, Angeles Forest, Big Tujunga, Red Box/Mt Wilson ... that are great rides as long as you don't mind sustained climbing. The National Forest starts in La Canada/Flintridge, but decent places to start/end a ride are either Pasadena area or Griffith Park area. I think these roads are probably okay during the week, though I've only ever ridden them on the weekend.
2. (way East) ... Glendora Mountain Road. I never ride that far East, but supposed to be great. Can start in Pasadena, but you have to slog through some not very interesting stuff first.
3. (West) ... Malibu. There are a ton of great rides in Malibu. Unfortunately, you need to ride the PCH to get to most of the canyons. On a weekend morning the PCH is beautiful, but other than that it's has alot of fast moving traffic. However, the canyons in Malibu should not be missed. If you search on ridewithgps or mapmyride you'll find a bunch of rides. The key canyon names are Topanga, Fernwood, Stunt, Piuma, Latigo, Encinal, and Decker. Almost all of these rides start in Santa Monica.
I'm a member of Velo Club LaGrange and I think a few others on WW are as well. Here's a link to some rides from the LaGrange site: http://www.lagrange.org/rides.htm
Also, here's some info on the Malibu climbs: http://www.lagrange.org/local_climbs.htm
The one hill I would not miss, no matter what, is Latigo.