This is our favorite spot to stay in Cape Town. The location is unbeatable, as you can just walk down Kloof St, to some of the best cafes and restaurants in town - yet it's on a side street that feels private, and is in general relatively quiet. What really makes it, though, is the staff at More Quarters - who have always been superbly helpful and accommodating.
Maybe worth keeping in mind for future visitors: this is actually a set of apartments that are managed together, and you might not stay in the exact one you booked. But from what I've seen they're all really nice, and the staff on site can generally accommodate requests to change if necessary. Also, the wifi connection can be a bit inconsistent - though it seems to be improving.