There is a small campsite on the left as you drive from Hunstanton and through Fornham.
There is also camping at Burnham Deepdale.
If you want a pub, the Queen Victoria at Snettisham has a CL for £15 a night.
Having said that, if you are a bit necky, there are no end of laybys and beet pads all over the countryside around you could discretely pull into just before dark.
You can park up at Hunstanton along the cliff road during the day, but not overnight.
You won't get into the Old Hunstanton (lighthouse) carpark at any time due to height barriers.