Holiday in South Africa (Cape Town)

I wonder if anyone can help me. I am coming to South Africa with my wife and 3 kids (2, 6 and 9). I arrive on the 27th of December and leave on the 19th of January. I do not have a big budget and would like to find an apartment to rent for 7 to 9 days in Cape Town from the 27th. Does anyone have any suggestions on were I should look and the costs or does anyone have an apartment I can rent.

Also I would like to take my family on a safari. Again I do not have a big budget any suggestions?