Get on the red bus tour from the Waterfront for a great snapshot of the whole of Cape Town. You can hop on and off at the stops - Camps Bay is a great stop for beach and bar/cafes.
Go up Table Mountain, take a trip to Cape Point and Boulders Beach and do a wine tasting tour. You can also do Township tours if that's your thing. All bookable at the Waterfront where there are loads of shops, bars, restaurants etc. Head down Long Street at night if you like bars and music.
Highly recommend Royales on Long Street for awesome burgers of all varieties.
That will give you a good taste of Cape Town in a short time. about 8 years ago
Helen has very good advice. I was there about a month ago and did many of the the she suggested and had a great time.
You should also try high tea at the Twelve Apostles Hotel (and try their amazing spa!)
I ate really well at the V&A Waterfront, you can't go wrong there.
Things I'd never hear of til I arrived in South Africa that I would recommend eating: grape and apple tizer (sparkling juice), biltong (a way better beef jerky), malva pudding (kind of like a sticky toffee pudding). about 7 years ago