If you are interested in hiking, Cape Town also offers some excellent trips that can be done in less than a day. Then I would recommend starting with Lions Head (easy/just a couple of hours), then go up table mountain and take the cable car or rappel down (medium/almost full day) or cross all the Twelve Apostles (hard/several days). You should be able to see all the way to Robben Island from all of these places and get a great view of Cape Town.
But the ultimate daytrip from Cape Town is to go south to Cape Point visiting places as Fish Hoek and Simons Town/ Boulder Beach along the way. I’ll write an own post about this coming up in a few days..