The Mt. Hollywood Trail has a few different trailheads.
http://latrails.com/ has a map of Griffith Park.
They do not show my favorite, the Wildwood Canyon Trail. It's in the Verdugo Mountains, but I think latrails.com temporarily removed it from the map because it was closed after the fire. They re-opened it recently. It's very steep, probably the steepest urban trail in LA. If you head north on Magnolia through Burbank all the way to the end, then make a left, then a right up Harvard, by the golf course, there's a park near a gravel parking lot. The trail starts near the entrance and really climbs. It follows a ridge up to one of the radio towers.