The 1,266 foot elevation Mugu Peak is at the western edge of the Santa Monica Mountains, in Point Mugu State Park. The peak provides views stretching from the Malibu Lagoon/Naval Base Ventura County and Channel Islands on the west, Thornhill Broome Beach on the east, La Jolla Valley on the north and more.
There are multiple ways of getting to the peak. The most direct (and albeit steepest) ascent is via the Chumash Trail, accessible across from the Naval Base shooting range (yes, sometimes you will hear rounds). The Chumash Trail is accessible off of PCH at this link. Look for the left turn into a small dirt parking area that has space for perhaps 15 or so cars.
The 7/10ths of a mile hike up the Chumash Trail is pretty brutal, but I've seen all shapes, sizes and ages making it up at varying paces.
So you've reached the top of Mugu Peak, enjoyed the panoramic views, saluted the flag on display, checked out the toolbox under the flag with logbooks and other items, the next choice is, do you go back the way you came or do you take another route? If you head back the direction you came, the title mileage of the hike is about 2 1/2 miles of mostly steep up/downhills.
Well, if you continue in the direction of Thornhill Broome Beach (southeast), you can continue on the Mugu Peak Trail, which is several miles traversing around the southern, then western sections of Mugu Peak. This is my preferred approach as the footing is much easier and your total mileage is roughly 4 miles. Plus, you are treated to additional views that are just beautiful.
You can also get to Mugu Peak from the La Jolla Canyon Loop Trail.