Access: I've read a lot about the road leading into this campground/trailhead area. There are two different ways to access it from what I can tell. I came in from the north (despite coming from I-40). Googlemaps took me all the way up Hwy 181 to Gingercake Rd, in the Gingercake residential neighborhood. From there, it is about 7 miles to the Table Rock Picnic Area. Approximately 5 miles of that is compacted gravel/dirt road. I did this in a Honda Accord. You DO NOT need an SUV or 4wd to do this route. You do need patience however. There are some spots where rocks are sticking up and if you don't have tires designed for SUV's, you could risk a puncture. There are some potholes to dodge and some washed out areas. All of this can easily be navigated. I saw a Prius that had made it up. Again, I did this with an Accord with zero issues. The last two miles is a relatively steep paved road. The alternative route up (which you pass on the way to how I went) is about 13 miles off of Hwy 181. I think this is the way that many people go and review that it is very rough. It brings you up to the Picnic Area from the south. The two ways merge just before the paved portion.
I should note that there are campsites all the way up once you hit the dirt portion of the road. Several of those campsites would be good options getting to the northern portion of the gorge.
At the Picnic Area, there is plenty of parking, a bathroom and well, a picnic area with tables and grills. To the right is the trail to Table Rock and beyond up to Hawksbill. There are no campsites, at least not to the point where you go up to Table Rock. To the left is the picnic area and then the campsite area. I would estimate there are at least ten spots where a tent could be pitched with an accompanying fire ring (made of rocks). This is on the ridge heading up to The Chimneys. I was there in winter and there were still at least four sites taken, so in summer I imagine you would have any privacy for what that's worth.
I stayed at the site further up on the right (they aren't numbered). This was the last spot before you really hit the trail (which by the way is immediate world-class views. I don't know if it was just in my head or not, but the winds were extremely high that night and it felt like some of the sites a little way down the hill closer to the parking lot (maybe 100 yards) had less wind. Not sure if that was real or not, but you may consider that a lower spot. All of the sites are between 100-400 yards from the parking lot. So no need if you decide to bring more than you might need.
Overall, can't recommend this location enough. Bring what you need though. There are not facilities and the nearest anything is essentially an hour away in Morganton.