Turns out options are limited to mostly Big Sur. Luckily, there are a tremendous amount of trails and campgrounds in the area.
A good place to start looking for camping in the Big Sur is their hiking page. This lists their backcountry trails, some of which allow dispersed camping. Big Sur wilderness falls into two categories: Los Padres National Forest, and Ventana / Silverpeak Wilderness. The best information regarding camping sites, trail maps, and etc were on a privately run site tracking trail conditions for Ventana / Silverpeak Wilderness.
For an approachable, oft-traveled, and well-documented route, your best bet is the Sykes Hot Spring route on Pine Ridge Trail. This is not true dispersed camping, but there are several large campgrounds on the way up that allow wood-gathered fires, and when we were there we were able to get far away from everyone else.
Other than Pine Ridge Trail, there are many other trails and campgrounds dispersed throughout Big Sur, this map allows route planning in more detail.
For our trip, the Big Sur fulfilled best my objectives for our vacation. While it wasn't truly dispersed camping, it was very close to the idea in that there were few people out there (and this on Memorial Weekend), we were able to hike for many miles into a beautiful wilderness, we were able to cook on a gathered-wood fire, and there was regular access to relatively clean water from the river cutting through the trails.
EDIT: (March 2017) Most of the Big Sur is closed due to wildfire. This information is out of date until those areas open. I am unaware of any places within the area now that fulfills the above objectives.
EDIT: (Jun 2018) Some of Big Sur is opening again! Do plenty of research beforehand to double check: http://www.ventanawild.org/trails/ventana-wilderness-trails/pine-ridge-trail Lots of fire restrictions as well.