Here are all the places you can find luggage storage in Cape town:
Cape Town International Airport.
There used to be a couple of luggage storage facilities at the airport that were set up during the 2010 world cup but right now most of them are closed. Most internet articles that are outdated will still refer you to these closed facilities.
Currently, there's only one luggage facility at the airport that I know, A-Teck. To get to A-Teck offices:
Walk outside the main airport building on your way to My Citi bus parking area.
A- Teck is opposite the police station right outside the terminal.
Luggage storage cost
Luggage storage cost depends on the number of hours your luggage is stored at A-Teck.
0-5 hours ZAR 70
5- 12 hours ZAR 80
12-24 hours ZAR 90
You can store your luggage here for a couple of days, you'll discuss the price with the management.
A-Teck is open from 6 am - 10 pm.
I'd totally recommend Bag drop, it is within the city center at shop 3, The square, 50 Buitenkant street, 8001 and is easily accessible from the airport via M3 route.
Luggage storage price: Since Bagvdrop store luggage in lockers storage cost depends on the licker size you use.
Bagbnb have a couple of luggage storage centers within Cape town.