If you have a car, there's a ton of options within 15-20 minute drive.
Griffith Park is probably the easiest bet. You can Park by the Ranger station and either run on the flat trails around the gold course, or else up an into the hills if you want a view and all that (http://www.modernhiker.com/area-maps/griffith-park/).
Another close by option is to run on the Arroyo Seco. It's got a nice trail running along the creek and up past the Rose Bowl and into the San Gabriel Mountains if you're looking for a long run (http://www.ci.pasadena.ca.us/PublicWorks/Arroyo_Trails/).
There are a lot of trails in the Angeles National Forest if you're willing to drive further and want to run a lot of uphill.