Cape Town tourist hotspots (including vineyards) are fine to do solo. Travel by car when you have to traverse the city. Uber is readily available. You can also rent a car, driving is great, although it's left side and most cars are stickshift. Automatics can be found but are pricier. Dunno what people say about driving, Cape Town has first world infrastructure and traffic was more law abiding and orderly than any Northeast US city I've been to. There are beautiful places to see around the Cape.
If you feel you will stand out as a tourist, then walking or hiking in the city is best done with groups. I stick out like a sore thumb in SA and definitely had some sketchy encounters when I walked out solo, but I guess we tourists corral ourselves into a small part of Cape Town and the criminals go there to prowl. However the popular trails in the city are probably busy and I saw plenty of solo headlamps navigating Lion's head at night, so I'd guess it's reasonably safe. At night I stuck to the waterfront or hotel. There are popular nightlife neighborhoods downtown (Long St.? Observatory?). All these places, especially waterfront, should be safe and busy at night.
Cape Town is an amazing, beautiful place, GO SEE IT, but I got a strong sense of "security vigilance" while there. It's something to keep in mind.