You're not giving yourself much time are you? Don't stay in central Cape Town. Would suggest V&A waterfront - good hotels, restaurants, cinemas, shopping, boat trips, street buskers, helicopter rides etc.
Alternatively Blouberg area which is about 20mins drive from the City but gives you that "classic" postcard view of Table Mountain across the Bay. Dolphin Beach hotel is pretty good and you have restaurants, bars in the vicinity but the water can be chilly (Atlantic).
See also Century City - very few places like it in UK except Trafford Centre. Join the penguins on the beach at Boulders Beach near Simonstown. When you go to Cape Point take the drive along the coast via Bantry Bay/ Hout Bay and along Chapmans Peak Drive. Oh and when you first travel from the airport be warned you will initially see a lot of the poorer community so don't be put off by first appearances.