Guangzhou is the third largest city in China.
West towards Nanning.
There is a toll gate at 22.747377,108.271414 which is easy enough to get to and is good for getting a ride. Use Google Maps to find the metro and bus routes to take. Once there, a sign is useful because the spot is also an unofficial long distance bus stop and people will presume you're flagging a bus if just thumbing. We'd recommend only trying to get to Yunfu from this spot which will get you to the first petrol station on the toll way and from there, you can petrol station hop all the way to Nanning. Once we got a sign to Yunfu sorted, we got picked up within 10 minutes.
We camped right next to the toll gate in a little triangle shaped park. It has comfortable grass, and no one much cares. Just be careful of "landmines."
There is a pair of easily accessed on-ramps about an hour and a half walk north of the airport. One from the east and one from the west leading to the same tollgate. There is a little walled "oasis" between the road and the carpark for the local shops and restaurants. If it gets late you can camp under the palm tree and nobody will bother you.
The tollgate staff are not friendly and told me I couldn't be on the on-ramp. Unfortunately, though the on-ramp is clearly signed for Shaoguan (韶关) which is on the way to Changsha, it seems nobody using this on-ramp is going that way. One friendly local suggested I aim for Conghua (从化) instead.
Alternatively you can look down the access roads and find a way to climb up to the expressway. Be careful if you have to cross the expressway like I did! I got a ride in a couple of minutes this way.