Down on the Lizard is wonderful but Roskilly's icecream is a great place to visit, lovely farm, laid back, peaceful and gorgeous icecream. On the way stop off at RAF Culdrose viewing point on a flying day.
The Minack is fab especially when a school of dolphins swim by behind the stage, it suspended the play when I was there!
Go to Sennen in the evening for the most amazing sunset.
Walk some of the coastal path for exploring more remote coves.
There are lots of Celtic stones etc, get an OS map to find them.
Logan Rock is a great place and there is a great beach that is a climb down so doesn't attract the usual beach crowd, from memory you have to go through the camping site which is also a good site.
+1 for the park at Marazion, spent many happy times there.
As said before a trip to the Scilly's is fab, the helicopter is fun.
St Ives is lovely, Tate is a good hit, but the town is busy.
Enjoy! We're going in August, I married a Cornishman so know it well and love it dearly.