An absolute must when you are in Cape Town is to take the drive all the way down to Cape Point where it is argued the Atlantic and Indian oceans meet.
The most south western tip of Africa is definitely worth the 1 hour and 20 minute drive from Cape Town especially if you are staying closer. The entrance fee is for a whole day enabling lots of exploring of the park including getting up close and personal with the resident ostriches, baboons and other wildlife.
The funicular isn't needed if you are reasonable fit and healthy as the walk to the highest viewing point isn't too strenuous and there are soo many photo opportunities on the way up. Spot how far away other popular tourist destinations are as well as whales and the next piece of land - Antarctica! Hint? It is very very far.
Make sure to take the time to explore the other picnic spots and beaches nearby too. It is a great day out if you are staying in nearby Simon's Town (around a 30 minute drive) or Kommetjie (around a 40 minute drive).
* Also a final tip for you - it is ALWAYS windy at Cape Point!