In reply to mlmatt:
Agreed.
Take plenty of water bottles and fill up at the North Stack visitor centre or the toilets at South Stack. Fill up before they are locked overnight.
I think there is a proper (basic) campsite at the foot of the South Stack road. Not that far to walk. Look at a google or OS map.
I am sure you will find somewhere discrete to wild camp hidden away from the dog walkers.
There used to be plenty of tents in the 70's at the above locations. Most people now have campervans or quick overnight tent pitches.
I can particularly recommend the grass next to the seaside prom shelters.