Rev, I really hope you enjoy your short visit to the Western Cape.
I agree it's a bit whistle stop. You'll be seeing a lot of the Cape from a window driving past but at least you will see further than the city bowl! For eateries, the V&A waterfront meets your needs - a bit touristy but reasonable prices and a really nice atmosphere with lots of places close together.
With regard to hiking Table Mountain, obviously you may not get clear weather or more importantly low winds that make the India Venster route dangerous and stop the cable car from running, so you either need to be flexible or accept you may not get those views in the short time you have. Unless you are going with a local / guide, I would recommend the Platteklip Gorge route because it is so much easier to navigate.
I also have to note that I wouldn't personally chose some of the 'activities' you have listed, because of the methods used to lure, train or 'domesticate' animals. YMMV with what you find acceptable. (The treatment of elephants where riding is offered is well known to be cruel in order to make the elephants obey their handlers, just search the web. Similarly to the 'lion petting' places where there is growing evidence of involvement in the trophy hunting business. On a lower level, I also don't like the practises of shark cave diving because the sharks have to be lured towards the ship! Whale watching is so much more pleasant because the whales come towards you when they feel inquisitive.) I realise that not everyone is interested in these aspects and I don't want to come across as 'preachy', I just hope anyone reading this forum would go away and research these places for themselves so they get an honest view of what they are offering.