Anywhere on the Lizard will be fine. If you are going self-catering, than you will want some shops near-by and Penzance is just down the road, and its a nice town anyway...Newlyn and Mousehole are close by.
Kynance Cove and the other coves on the Lizard will keep you occupied for a week at least. You are within striking distance of both the North and South coast of Cornwall.
But if you anything in school holidays periods, they may be already be snapped up. September would be a nice time to go.