locally, your best bet for solitude and some basic amenities would be Lupine, Campground.... 9 miles out Blue Ridge Rd (which is broken pavement- then dirt... but usually OK for most vehicles)
You're not going to find showers at any campsites on the Angeles Forest. But there are fire rings, picnic tables and pit toilets at this location. Bring water, as there is none down there... as well as your Adventure Pass.
If that's too rough for you, many of the other campgrounds in the area are pretty quiet during midweek.