soooo much to see there. Table Mountain is a must do, and there is also Lion's Head and Signal Hill. You can even go paragliding off of Lion's Head. For beaches my favourites are Clifton, Camps bay, Muizenburg and Simons Town. Definitely go to Simon's Town to see the penguins. Muizenburg has a lot of surfing and Camps Bay has a lot of restaurants and more of a Miami feel.
Your trip wouldn't be complete without going to Robben Island, it's a must do. Also check out the District 6 museum or one of the Iziko Museums.
Other places to visit: The V and A waterfront, the Company Gardens, Long St, Green Point, the football stadium, Green Market square, go to stellenbosch and go wine tasting, go on a safari, go to the old biscuit mill, take a tour on a double decker bus, go out to cape point, visit the aquarium, etc. SO MUCH TO DO! about 7 years ago
This would be great reading for you - please don't do this in 24 hours; I personally think it is not possible, but you can get some great ideas.
If you can get out of Cape Town a little it would be well worth it to go whale watching in Hermanus, Shark diving in Gansbaai or wine tasting in the Cape Winelands. about 7 years ago
There are really great attractions mentioned above. Don't forget to take a day or two to explore the Cape peninsula. This runs from the eclectic seaside harbour suburb of Kalk Bay all the way past the fishing village of Fish Hoek and into Simon's Town where you can visit Boulders Beach and its penguin colony. Further along the route you'll reach Cape Point which is the peninsula's southern most tip: the area which is said to be where the Indian and Atlantic Oceans meet.
In Cape Town CBD you can also take a tour of the Castle and take a ferry out to Robben Island for a tour of the place where Nelson Mandela was imprisoned.
Enjoy! about 7 years ago