Backpackers is a great budget accommodation in all three cities.
Jo'burg: Joburg Backpackers - great for organising day trips and tours. Friendly atmosphere: http://www.joburgbackpackers.com/
Cape Town: Cape Town Backpackers - really vibey, friendly and clean with great reviews: http://www.capetownbackpackers.com/
Durban: Nomad Backpackers - They have a pool, a bar and a very chilled vibe. http://www.nomads.kzn.co.za/
Hope it helps :-) about 6 years ago
Hi - I will answer the Cape Town section of your question !
You could always try the Daddy Long Legs art hotel/apartments in the city centre. It's really funky - not sure what your budget is, but check out their site here: http://www.daddylonglegs.co.za/Hotel_Rates.html
Also, it depends on the area you are wanting to stay. Atlantic Seaboard/city centre/Waterfront is probably the best for a short stay - great beach views, proximity to the city and plenty to do.
Have you an idea of where you want to go in Cape Town? about 6 years ago