Cape Town to Jhb is a long way so even without detouring much you could stick to either of the 2 main options - via the N1 or N1 + N12 via Kimberley.
The "nothingness" of the Karoo is part of what makes it special and beautiful.
I would recommend any of the following stop overs:
- Swellendam (might be too close). Lovely atmosphere, eateries, art... and historical "Drostdy" Museum but you can skip that if you're not into history/culture. There is a nice farm outside where you can stay or the Bontebok national park.
- Graaff Reinet itself, for the nice feel of the place, history and beautiful surrounding landscapes.... (valley of thousand hills) (can sleep at Camdeboo national park) or something really special/off the beaten track and a worthwhile detour: Nieu Bethesda (must visit Owl House)
- Richmond on the N1 (the only booktown in South Africa)
- Detour to Clarens & Golden Gate (could easily do 2 nights) - beautiful landscapes, hiking, the village of Clarens is arty and nice atmosphere. At Golden Gate you could visit the vulture "restaurant" and hope for the chance to see the endangered bearded vulture (one of the best places to see them).
- If you choose the N12 rather, Kimberley has the "big hole" and the dam there has one of Africa's few lesser flamingo breeding colonies which should be something to see this time of the year.
Sleeping under the stars, Tswalu in the Kalahari (north of Upington, near Botswana border) has a "star bed" but very $$$.
I found the hammock camp I first thought of when I read your post, but unfortunately it's not in the right area. It's in Limpopo :(
Kagga Kamma lodge in Cederberg area (the whole Cederberg area is a fantastic location anyway) has open air beds and cave option, but also a bit $$$.
Anysberg nature reserve near Worcester, does stargazing from a platform. They have a camping ground... not sure if you are allowed/would want to, just sleep under the stars in the camp ground? Or buy yourselves those very light (parachute material) hammocks? (Thinking of this option, Mokala national park near Kimberley campsite might also lend itself to this, private camp site with own shower/toilet room and kitchen facility (incl fridge) per site, electric fence to keep the buffalos out), the 6 sites overlook a waterhole where animals may come to drink night and day.
I think you might find this article interesting - Stargazing locations/activities.
(I also love sleeping under the stars and keen to do so again, so am 'penning' down as I go, you have got me onto something now!)
Carnarvon is also on my wish list for a stay at the Corbelled Guest House (no electricity), also in that area there is a farm full of windmills (the owner is a collector, i beleive).
Usually when we do that route (I also love road trips) we stay over at the national parks (Mokala, Karoo) because we love wildlife & nature, and you know the quality you get in the national parks, it's safe etc.
Enjoy! I am now green of envy although I will get my opportunity again.
Wilma