Cape Town is absolutely stunning, you'll have a wonderful time there and there's loads to do.
We did a day trip (this was organised through our holiday company but I'm sure you could sort locally) down to Cape Point which was just the most stunning scenery, with a boat trip to see the seals and a visit to Boulders Beach for the penguins, fantastic experience.
We went up table mountain which was great but take a jumper, it was cold up the top! We also did paragliding off signal hill landing down in camps bay.
We used the hop on hop off bus which was a great way to get around, and visited the botanical gardens which were lovely.
A bit of beach time down in camps bay, as the sun set.
Use Uber to get around, it's safe and really cheap. I researched restaurants on trip advisor and we had some great meals out at great prices. We had a great experience at Mzansi but read the reviews carefully so you know what to expect and see if it's for you.
If you're not going there separately I'd recommend a visit to Franschhoek to visit the vineyards using the wine train, a lovely experience, stunning scenery and very cheap wine!
The V&A waterfront is nice for a mooch around and lunch.
Be careful, but enjoy, it's a spectacular place!