I have a very good friend on Tenerife and her daughter wants to go to La Gomera, and they would like to stay on a campground.
As much as I know, on La Gomera there is just one campground… but I have heard, that if you go with your tent to another place, that’s also no problem. But never go with your tent inside the nationalpark…. there camping is not allowed 
La Gomera a nice place to be… of cours a bit quiet…. but nice 