If you want to give your credit card some exercise, head out to Long Street in Cape Town City Centre. It's also full of great shops and restaurants, so you can spend the afternoon having a wander. Splash some more cash at Greenmarket Square, Bree Street, and Adderley Street.
You can learn about the history of Cape Town with a visit to Castle of Good Hope. Wander the seaside or discover the area's mountain views.