You probably have seen photos of the Christ of the Abyss (a submerged bronze statue of Jesus Christ with his hands outstretched) which you can actually scuba dive down to see up close, but San Fruttuoso is also the most perfect day trip from Portofino to stay on land and dine.
Hop on a boat (they run hourly) and eat lunch at any of the spots surrounding the cute Benedictine monastery here. Because it houses no (real) hotels and isn't a port, the guests that make the journey out are basically tourists coming to see the Benedictine monastery or just to lounge around. This would probably be the sort of thing we'd find annoying were we anywhere else on earth. Here, even the tourists were totally charming....