You can easily spend two or three days in Cape Town city alone - ascend the revolving cable car of Table Mountain by day (and Signal Mountain by evening or night) for an idea both of the city's size and its ocean-side orientation and a walk through the fynbos and views of the Lion's Head; mosey around the Victoria and Alfred (the Queen's second son, who tipped the first load of stone into the sea to initiate construction of the harbour) development on the waterfront with its world-class aquarium, shopping facilities and huge variety of restaurants, as well as historical connections; visit Company's Gardens with the Parliament Building (CT is teh country's legislative capital) or St George's Cathedral or the excellent museum-cum-stately home within the castle; or take a more humbling trip to Robben Island (overcrowded in these days of Mandela-worship, but nonetheless worthwhile) or perhaps a guided tour into the Cape Flats...and this is all before you head out of CT proper into the winelands and around the coastline.
Quick Tips:
Keep an eye on Table Mountain for a likely clearing in the cloudy "tablecloth" -- views come and go and it's no fun if you pick unwisely. You can hike up to the top for free, but the revolving cable car (though pricey at 105Rpp return) is an experience.
Cape roads and attactions get crowded at weekends -- apparently peak summertime traffic stretches for hours. Also true of Hermanus/the penguin haunts of Boulders' Beach.
V&A is CT’s pickpocket hotspot -- keep safety concerns in mind but don't get hysterical about it. Avoid public buses and dark streets, take care on arrival not to drive inadvertently into the Cape Flats near the airport; don't stop the car unnecessarily on highways, or hitch-hike.
If you don't fancy staying in Cape Town itself, there's a good selection of B&Bs along the west coast in Hout Bay or Clifton, where you get a great view of the twelve Apostles and access to splendid beaches.
The classic picture postcard/photo opportunity of Table Mountain is NW, from BloubergStrand. On a lovely beach, paddle in Antarctic-cold water while watching wetsuited parakiters bump across the waves.
Best Way To Get Around:
Scaremongerers warn that driving in CT is nightmarish and parking worse; it’s not that bad -- there are decent carparks (some with guards) at Signal Hill, etc., and parking meters, attended by helpful traffic police, on the streets by Companys Gardens (6R per 30 mins). Overnight though, check that your hotel has off-street, secure facilities (may cost more but likely to be worthwhile given the level of nighttime car-crime).
At the airport (15 miles/24km), there are car rental agencies or you can come into town via taxi/public transport. Taxis cost cR180; 20-30 mins. Apparenly, airport shuttle buses leave every 30 mins for the train station, SAA city terminal and major hotels for R15 but aren’t always reliable.
Once in town, getting around by public transport is also hard work -- avoid the packed buses, instead spread your Rand by taking taxis -- but remember that some buy up knackered bangers and hawk themselves as taxis (in uninsured death-traps). It sounds a touristy cop-out, but get a hotel to order a cab rather than jumping into one ad hoc on the street. An average trip - say V&A to the castle - should cost about 30-35R.