Hi there,
Lived in Cape Town a few years (native South African), but left 3 years ago, so my info might be a bit outdated...
There is a very good aquarium and oceanarium, might be fun for the kids.
Very nice day trip if you'r renting a car: over Kloofnek, via Campsbay,Llandudno, Hout Bay, Cape POint (part of a national park, my sister and I got very lost there once and was chased by ostriches, we walked a trial and got lost!), look out for the crosses at the Cape of Good Hope that the sailors used to navigate with (they lined them up, might be fun for the kids), back up to Fish Hoek/ Simons Town (Boulders' Beach for penguins, watch out, they seek out shade under the cars in the car parks, but the car watch will usually keep a look out for them) . Can totally be done in a day, I did this trip many times with friens visiting from abroad, there is also an ostrich farm somewhere along the way, nice shop with ostrich leathe rproducts but VERY VERY overpriced. If you're in self-catering accomodation, time your trip so that you stop at Kalk bay at around 16:00 - 17:0 when the fishing boats come in, buy fresh snoek (large gamefish) or whatever they cought that day (snapper, red roman), not expensive and direct support for the local economy, they will gut and clean the fish for you too for about R5 extra, and have a barbeque that evening! Then cut across over the peninsuala back to Cape Town.
Kirstenbosch Botanical gardens lovely. Take a picnic.
Trip to Robben Eiland worth doing, a bit of history, boat rip might be fun for the kids. On the island itself you are driven around in a coach, only 'walk-around' time you have is back at the prison blocks and around.
Spier is very touristy, but kind of nice. Book dinner in a tree house. I thought it was expensive, but worth it. Beware of the road between the N2 highway turnoff and Spier, narrow, potholes, pedestrians.
Stellenbosch and Franschoek both lovely. (I got married in Franschoek, so am perhaps a bit partial...
Buyyourself a John Platter Guide if you're planning to visit the winelands, from any newsagents, very handy. Wine farms worth visiting: Vergelegen (think they were affected by the recent fires though... not sure), Boschendal, Lanzerac, Thelema for the best Pinotage and Cab,Constantia, lots of beautiful wine estates, these are the older and more well known ones, wine estates usually well signposted, most (almost all) have tasting rooms, either free or nominal ffee...
Hillcrest Berry Orchards for a good lunch (just outside Stellenbosch)
I can go on all night, but can't think of any other child-friendly things... sorry!
(will post if I remeber something)