I've been on two trips so far, but I've had some awesome experiences!
The Pine Canyon campsite #4 is awesome. I spent my very first night in BB there. This was at the new location (away from the trailhead). I wished the damn map had been updated because my wife and I thought we were camped right next to the trailhead. Note that the map we were given at HQ (Sept. 2004) showed the campsite AT the trailhead. We begain our hike of Pine Canyon from the campsite, and it's probably almost 1 mile from the trailhead! (i.e. our fabulous Pine Canyon hike was about an extra 2 miles longer than necessary!).
Anyway, PC4 has amazing views and provides much peace and isolation from the world. Sunset and sunrise there was awesome because of the long distances you can see and all the mountains that pretty much ring the horizon.
http://www.texbrick.com/photo/bb/bb_pic03.jpgErnst Tinaja #1 is great. It's in close proximity to the trailhead (could be a bad thing during busy times) so you can hike into the canyon directly from the camp. There's a small hill to the west that once climbed, offers awesome views of the Chisos.
We had a nice visit here, despite getting a flat tire and then being surprized by a very stealthy park ranger. We were eating dinner after sunset and all of a sudden became aware of a man walking towards us! I nearly choked on my food, which was a good thing becuase it prevented me from screaming like a little girl. But he was friendly and just wanted to check on us and look at our permit.
http://www.texbrick.com/photo/bb_trip_plan/et_8.jpgThe Elephant Tusk primitive site looks pretty nice, but I didn't stay there. I parked near there to start an overnight hike to the peak. Here's a shot that's somewhat close to the campsite:
http://www.texbrick.com/photo/big_bend2/details_text/bb2_dt_04.jpgThe campsite is right across the road from the trailhead, so it was a little busy because of people who parked there to go hike up to the peak. The campsite reminded me some of PC#4- it's in a very open, flat stretch of country with mountians off in the distance 360º.
Of course you can always haul your stuff about 4 miles down the trail and camp close to the peak :D
http://www.texbrick.com/photo/big_bend2/details_text/bb2_dt_13.jpgI go to Big Bend for the scenery mainly, but also for the peace, quiet, and solitude (hey, who doesn't? :D ) I think that any backcountry site that is remote and tough to get to will be a pretty good site. I'd like to try the campsites at Telephone Canyon, Willow Tank/Ernst Basin, Glenn Spring, Juniper Canyon, and Dominguez Trailhead. Of course with Zone camping rules, you can camp just about anywhere outside the Chisos!