There's very little to see in Jo'burg and it's much more expensive. In Cape Town you can save money by spending a week on the beach, which is free!
If your budget allows, you should go up the west or south coast (the "Garden Route").
Coast2Coast is
the definitive budget (backpacker) tour guide to South Africa.
The
Baz Bus is a low-cost tourist bus; much safer than alternative long-distance buses!
Downhill Adventure has some awesome day-trips and activities that'll blow your budget faster than you can say "Table Mountain."
Here and
here are some more hints for something to do.
Really, a trip to Cape Town isn't complete without a trip to
Robben Island and a
township tour.