You can probably camp at Pyramid Lake, down the hill from the Water Project Museum at Vista Del Lago. The museum is worth seeing, and has clean rest-rooms and lots of space to park. There's fast food at the Gorman exit. There are good outlet stores and a food court just before you start the ascent from the North side, I usually take a break here before going up the grapevine:
http://www.tejonoutlets.com/
Ft. Tejon historic park has restored adobes and re-enactments, and is another place to camp. And of course all of LA is to the south.