My teens both spent a term in a South African school and we have holidayed there too.
Yes, there are water shortages but you can plan for future travel. Hopefully there will be rain. It is also a big shame for SA economy if no-one goes!
I would suggest Easter Holidays is the best time to go. It is hotter at Christmas, and a lot more expensive, and fairly cool in the summer holidays, but a lot cheaper! However, the end of our summer holidays is good because there might be whales in the area. At Hermanus you can see them at very close quarters from the coastal path. It's a real treat. There are boat trips out to Shark Alley too. This is not exactly Cape Town, but it is not that far. Teens would love that. You might find the tour operators have whale sighting logs so you can check out what they see and when. We saw lots of whales in early September.
Around Cape Town you have Robben Island, Table Mountain, the Waterfront (but you could be anywhere!), Chapmans Peak, Boulders Beach for penguins, Constantia Vinyard for Cape Dutch architecture, Cape Aguilas and lots of beach side areas such as Camps Bay, Hout Bay, Llandudno etc . Most of the suggestions above are enjoyable for teens, as long a they do not want theme parks!
You have a vibrant restaurant scene in Cape Town and many of the guest houses there are outstanding. The staff are unfailiningly helpful and you will get a lot of help and advice from guest house owners and managers about where to go, what to do and what not to do! They may well have local recommendations for you. I think the guest houses are far better than faceless hotels. They tend to be in fairly exclusive areas so you are safe too. As always with SA, you need to make your teens aware of safety but you do not have to worry too much.
It is a great place and I would recommend a visit to Stellenbosch too and Franschoek.