It's quite late to be planning the details although SA schools will be back so it probably won't be too manic.
If you want to stay around Cape Town, a few days in the winelands is obviously a good choice. There are loads of great farms you can stay at. Spier is nice for a mid level cost and is quite lovely - although Spier wine isn't my favourite so use it as a base rather than prioritising wine there! . But there are many and huge variety in cost etc.
If you've got a week in Camps Bay - you can use that as a base to explore the city centre, waterfront (shops, markets, restaurants, aquarium etc) while still enjoying lovely beach time. Take yourself for a drink or dinner at 12 Apostles or even a full day using the spa as well - it is one of the most beautiful spots in the world in my opinion.
Kalk Bay - which is on the other side - is also a great spot to spend a few days. It's more hippie than the Camps Bay side. Lovely beaches though, great restaurants and pubs etc.
I would agree though that going up the coast a bit is a good idea - Pearly Beach way going up the west coast, or Hermanus on the east. Or go further up the garden route to Knysna or Plettenburg bay.
Things to do in cape town outside of the wine, food, shopping:
Go to Kirstenbosch gardens for a day. Depending on when you are there, check out the Sunday sunset concerts as well - a really lovely evening in Cape Town in the summer.
Walk up Table Mountain. I think for tourists there are specific recommendations so check those. We used to walk up the contour path then across and down skeleton gorge, I think, but I'd get advice on this that's more up to date.
Afternoon tea at the Mount Nelson or at the Vineyard Hotel are both lovely.
Surfing at Muizenberg - I think you can access classes on an ad hoc basis which is super fun too.
District six Museum.
If you like cricket, check out if there are any intersting games at Newlands Cricket Ground - it's a fabulous day out!
Are you travelling with children? If so, can't recommend the Scratchpatch highly enough - one in the Waterfront, one in Simonstown. Aquarium is fantastic for kids too. Also Boulders Beach and the penguins. The Waterfront always hahs lots on for the kids and a lovely play area. Along the seafront at Seapoint there are a couple of good play areas - the blue train park is especially great (incuding the train) and the kids love it. My all time favourite picture of DS was taken at the Seapoint Swimming Pool - beautiful salt water pool on the Atlantic and worth a day out.
If you have a bit more info on the kinds of things you want to do, I can make more recommendations.