I just took a look at Capetown in the Mapquest app. It's down to at least street level. (I see what looks like really small streets, named.)
The app is free. Install it (or just look at their website mapquest.com - it looks like the same map) and look at the area you're going to and you'll see if it's detailed enough for you. (On the site you can put a from and to location and see if it gives you decent navigation.)
(I tried Maps, but Mapquest seems to have more detailed maps, at least in Capetown.)