The Cape Peninsula is one of those places on earth where it is hard to get bored. It offers so many alternatives to enjoy your free time that it makes it difficult to set priorities. Here are a few options but of course they are not the only ones. Investigate for yourself. You'll find many more.
If your wallet allows it, enjoy yourself with a helicopter flight. You will remember it forever. And if you're a brave and maybe want to gain another MOSTPOINT, enjoy the view from a (tandem) paraglider. You'll be at one of the best places in the world to do so. By the way, Gansbaai, not far from Cape Town, is also one of the sites chosen by adventurers from all corners of the globe to see the great white shark in its natural habitat. A “Unique experiences” MOSTPOINT. Do you dare to dive with them with Shark Cage Diving?
Discover the penguin colony at Boulders Beach in Simon's Town. If you do not like crowds, head to the beaches Bakoven and Glen near Camps Bay. On the first maybe you just want to lie in the sun and on the second you will want to get on a surfboard and join the seasoned surfers catching waves find.
If you prefer something more bustle, take a tour of the lively port of Cape Town where you will find many shops, bars, a Ferris wheel and the Victoria & Alfred Waterfront. Robben Island, notorious for being the place of detention of political prisoners during apartheid is directly opposite. Currently declared a World Heritage Site by UNESCO, you can reach it by ferry and visit the cell of prisoner 466/64, the Nobel Peace Prize Nelson Mandela.
Finally, if you want to take the opportunity to add another MOSTPOINT to your profile, hit the road and at about 250 km to the east you get to Cape Agulhas, the southernmost point of Africa. Look for details in the “Extremes of the World - Continent” category.