Pelle och Mia,
I live in Sweden, but I am from South Africa. I did not want to answer your question because my written Swedish is not that good - I thought I should answer instead in English. Sorry, but I hope this helps.
Cape Town is the best place to go if you want a bit of the city and enjoy restaurants and music. If you want to swim and sit on the beach, I would head up the coast of the eastern cape as the water is warmer there - just know that the towns are not as fun as Cape Town. If you went to Durban or Port Elizabeth you can easily fly from Cape Town for cheap. It only takes an hour.
A good resource in Swedish about what to do in South Africa is here
Resekalender Sydafrika – Vad man bör besöka och när - it is broken down by months, and should give you some ideas of what you can do.
Enjoy your trip.