Cape Town itself is quite a small city (or at least a small city centre because of the shape of the bay/mountain) and the suburbs don’t really have much in them. However, the bus tour gives a good overview of the city, its history etc. The tour of Robben Island is worth doing. If you wake up and the sky is clear, walk up Table Mountain – don’t plan it for a specific day in case the cloud is in!
Assuming you are hiring a car, if you are into wildlife, the penguins at Stony Point are lovely and it seemed a nicer viewing location than at Simon’s Town. Also the trip around the bay on the R44 is as pretty as Chapman’s Peak drive, IMO. If you drive to Cape Point, you will very likely see babboons and ostrich.
In the immediate area around the vineyards, its all about the wine (and brandy) with hiking in the nature reserves of the surrounding hills. There are some MTB trails near Klapmuts (here) but we didn’t use them so can’t comment.
Enjoy the hols, its a lovely part of the world.