I took my family (2 adults/3 kids) to SA in July for 3 weeks. Cape Town for 6 days.
--rent a car for sure. Very easy. We drove at night from Stellenbosch back to Camps Bay and I would do it again without hesitation.
--you do need clear day for Table Mountain. We took cable car up so I don't know about hiking. I think it is about 2-3 hours though.
--I kept hearing that Robben's Island had become rather touristy and the weather really wasn't conducive to a trip out there. If you want to see/hear about apartheid, you can visit the township in CT. We did not go there b/c we had already done a private tour of Soweto in Joburg.
--We spent 3 nights along the Western Cape before settling in Camps Bay (Cape Town), including Hermanus, and never saw a whale. I think July is the earliest you'd see one.
--Def do the Chapman's Peak drive to Cape Point with a rental car. It was great to stop at lookouts along the way.
--we did Kirstenbosch, too. There's a pretty restaurant in the garden for lunch, or you can take a picnic.
--if you have time after Kruger (and if you're driving back to JNB) you might drive through the Panorama Route to see various landmarks.
--we flew from CPT to SZK (Skukuza...inside Kruger). It was really cool to fly over the park and see animals from the plane.