Yes, Cape Town and the surrounding counrtyside is brilliant. We also went there on our honeymoon, in August 2003, and stayed for 5 nights, which was enough for a taster - we'll certainly be back!
Table Mountain is a must, for the best 360 degree panoramic views of the cape and city. We were very lucky and had a perfectly clear view, before getting covered in the 'table cloth' of cloud.
For safety, the Waterfront area is constantly monitored by CCTV cameras and police officers / security guards, in order to make tourists feel at ease.
We stayed in the Waterfront, at the Table Bay Hotel (fantastic in every way - ask for a mountain view), and felt very safe walking around, even in the dark evenings. The restaurants are excellent, and there are designer shops from across the world, but they are more expensive than in the city centre.
Taxis are easily available and very cheap - ask your hotel to phone one for you to be sure that you are getting a good company.
Our day trip to the vineyards of Stellenbosch was also very enjoyable, as was our day out down to Cape Point and the Cape of Good Hope NP. Simons Town was lovely.
The township tours are really only possible with a guide, but only go if you particularly want to see vast slums. We decided not to go, and just keep the good memories with us.
Unfortunately we never made it to Robben Island, but I believe that it is certainly worth it.
Price wise, we were more than happy with the local costs, but things are no longer dirt cheap. We bartered for our traditional handicrafts in Green Market Square which was fun, and came back with some beautiful hand-carved wooden bowls and leather coasters.
Another advantage is that there is minimal time difference from the UK, and most likely you will fly over night, and arrive fresh and ready to holiday.
Enjoy....