I'm from Liskeard, 20 miles on the better side of the border
I spend most of my time on Bodmin moor or Dartmoor.
Walker >> The South West Coast Path is massive, and covers the entire coast from Somerset (I think), right round to Dorset. As for the Cornish part of this, the North coast is far prettier - golden sands, beautiful views and consequently more tourists. The south coast is rather greyer and more shingly, but (especially at this time of the year) less populated.
Liskeard is on the south coast - a few miles from Looe. Looe itself is too busy for the kind of thing you're looking for, but Downderry a bit further on might suffice. It's a really long beach, if you head for the far end of it you're unlikely to see anybody during the day, let alone over night. (Although it is technically a nudist area!) You'd have to be really careful about tides here though 'cos they come right up and you'd be backed up against some loose, slatey cliffs.