Difficult to chose!
One option is driving. Car hire for a day will be easy and with advice from locals and maps:
With Table Mountain, even if you are unable to go up the mountain (low cloud, long queues {or vetigo}) then taking a drive up the mountain road is still VERY good. You can then drive across to Signal Hill. There is a car park at the end of the road. Usually very blustery up there but a fine sight across the city before you and out to Robben Island.
There is a circular route around the mountain that takes a number of hours but has brilliant views and you can choose lunch in many different places along the route. If driving, keep to main road and be back before night fall.
Within the city, I am not really up on the museums and galleries but they should be easy to find. Having been visiting the city for 41 years, I've got past the regular touristy things but looking out from the mountain and Signal Hill never fail.