As far as the five villages are concerned, we can be very short. There are no campings, where you can put up your tent.
North and south of the villages, you will find some campings in Levanto, Deiva Marina and along the Tuscan coast.
In Levanto there are a few campings :
Further north, you will find two larger campings in Deiva Marina. Both are located close to the nice sandy beach.
Specifically for Campers, the situation is not much better. The parking place, on the beach of Monterosso, is of course a beautiful location, but for the rest not too attractive.
Before entering Portovenere, at the roundabout, there is also a parking for campers, but without any further infrastructure. Good for a night, but not more.
In Levanto, on the parking behind the station, a few places are reserved for campers. But you will need to be very lucky to find a free place.