I've visited the Cape area on my own 3 times now, but not been for nearly 10 years. I saw lots of whales while I was there (and you will be right in the middle of the season for it too). Here's what I recall of my trips:
Lots of whales in Hermanus, but lots of people too. What I did was drive out along the coast east of the town on the main road, then down through the houses to the quieter coastal bit where you can sit on the rocks on your own and have the whales all to yourself (they were really close!) You also get a nice view of them breaching in Walker Bay from there.
Lots of whales too in Simon's Town - in fact I remember they were so close to shore the traffic just stopped to watch them. On the main road south of Simon's Town, there was a couple of laybys where you could pull over and watch the whales surface from the shore.
I stayed in Simon's Town itself for a few days and it was a great location for whale watching, accessing Cape of Good Hope Nature Reserve and also for Boulders Bay (I stayed in a former convent a short walk away from Boulders).
Regarding the nature reserve, higlights for me were wildlife spotting, sitting in the restaurant and eating lunch and watching a whale and her calf directly below me in the water, and walking between Cape Point and Cape of Good Hope. I think a lot of the coach party delegates don't get time to do this, but it's an incredible walk - halfway along is the very dramatic Diaz Beach and there were crowds of huge lizards sat on the fence just above the beach. The east coast of the park is also good for a coastal walk and there's a shipwreck along there too (the Thomas Tucker, I believe)
Don't go near the 'whale watching' boats departing from Cape Town itself - I foolishly got on one and was so seasick that by the time a whale appeared I didn't care (didn't actually care if I lived or died by that point as I felt so ill). The trip on an inflatable out of Simon's Town was much better!
Finally, if you come across a an official shark spotter on Boyes Drive, the road above Muizenberg, they should be able to tell you what's been seen out at sea that day (sharks and whales!)
Apologies if any of this information is out of date at all - it's based on my experiences 10 years ago.