There are a number of "trails" in the Verdugos, mostly on dirt fire roads. Here's a personal favorite that is actually mostly on trail and not on dirt road: The Fire Warden's Grove Loop.
Start at the turn out on La Tuna Canyon Road here: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG. There is a trail heading up the ridge that joins the remains of an old dirt road here: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG. This trail is a little hard to follow and had some downed trees on it last time I used it. It's also brushy. Once you get to it, follow the old dirt road through the Fire Wardens Grove -- a grove of trees planted by LA County Fire Wardens years ago. You eventually join the Backbone Road here: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG. Proceed west along the Backbone Road to this northward jutting point on the road: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG. Look for a trail going north from this point following an old road bed. Follow the trail down the ridge. It will leave the ridge approximately here http://www.topozone.com/map.asp?lat=34. ... &layer=DRG, still on the old road bed, and join the canyon bottom approximately here, where you will find the remains of an old car: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG. Follow the trail down the canyon bottom for a ways until the trail climbs west out of the canyon approximately here http://www.topozone.com/map.asp?lat=34. ... &layer=DRG and proceeds parallel to La Tuna Canyon Road along a flat faced ridge and drops down in to the next canyon to the west, meeting La Tuna Canyon Road, here: http://www.topozone.com/map.asp?lat=34. ... &layer=DRG near BM 1347.
The exit trail is weirdly laid out once you pass the wreck of the old car, but, hey, at least it's hiking.

These trails aren't marked on any USGS maps that I'm aware of, so I'm giving you approximate points from memory. The points are going to be pretty close, but there may be a little bit of nav. involved here; just giving fair warning. I'm choosing clockwise deliberately because the up trail is far less used than the down trail and locating the up trail's endpoint in Fire Wardens Grove can be tricky. The down trail that returns you back to La Tuna Canyon Road is popular with the Mtn. Bike crowd, and you shouldn't have too much trouble finding it or following it.
Alternatively, you can climb the dirt road from the 210/La Tuna Canyon Road interchange area, but then you've got a much longer walk on La Tuna Canyon Rd to your car, and you're on boring
