So many options….

If you are heading to the Western Cape, be sure to include Baviaanskloof. It is fantastic.
Also check out Die Hel (Gamkaskloof) off the Swartberg Pass. Lots of other passes round there too - if you want more info on them check out this site https://www.mountainpassessouthafrica.co.za/

If you have 3 weeks one option (which i have done) is fly into Windhoek (Namibia), go up to Etosha then pick your way down to South Africa via Sossusvlei (dunes) and Fish River Canyon on the sand roads. Then drop into South Africa for the above, linked into the Cape.

Not 4x4 adventure, but if you’ve not done it, you might want to pick up bits of the Garden Route too (eg Hermanus, Knysna).

I’ll leave others to comment on the East side.

I had planned a 3 - 4 week trip tour-guiding first-timers around South Africa and Lesotho, but had to postpone it due to C19
If you're interested I could send you the Garmin file which you could read in Basecamp or Mapsource and upload to a Satnav.
The trip starts and ends in Cape Town (Western Cape), takes you through the Karoo, across the most scenic mountain passes in the Eastern Cape, as suggested above through Baviaans Kloof, northwards into Kwazulu-Natal, up the famous Sani Pass into Lesotho and via the Freestate back to the Western Cape.
The daily distance ranges between 2 - 300 kms which takes into account that many roads off the beaten track are dirt roads. This leaves you enough time to relax in the afternoons. All legs of the journey are planned to end up at a place to stay, some are hotels, others are B&B's. No campsites.
I have done most of these routes over the past years on by m/c and suv, so for a 4x4 this shouldn't be a problem. Just remember that gravel isn't tarmac, so take the curves easy and not too fast


This trip will take you through the most beautiful South African landscapes. It includes remote and arid regions as well as lush coastal areas, plus some of the most spectacular mountain regions.

PM me if you're interested.

__________________
Only when we pause to wonder
do we go beyond the limits of our little lives.
(Rod McKuen)

So... if you're only doing a 2-3 week trip, AND doing it as a family so need logistics taken care of, AND you're not already experienced overlanders...

...go for the package tour.

I know it's against the spirit of HU but really, any money you save by arranging things yourself - if you will save any at all - is likely to be overshadowed by the amount of headaches you will endure. Just spend the money and get the experience you want without hassle.

I suggest aiming for 150 km/day and no more, especially since you note interest in culture. This keeps the time you spend getting from A to B to a minimum, giving you time to enjoy the destinations.

Although tempting to try to see a lot, I suggest picking no more than three nature reserves - Kruger is excellent, some of the small private reserves are very good, Addo Elephant is compact and you'll see (as the name implies) a lot of elephant.

Areas to consider to enjoy scenery include Cape Point, Golden Highlands, Drakensberg, Garden Route, Blyde River Canyon, and Richtersveld.

Cultural attractions include museums/galleries in Cape Town, Johannesburg, and Pretoria (lots more but I'm keeping this to a minimum), and (obviously) the wine country.

For a 3 week trip, I guess my sense is that you'd be best avoiding long distances, and suggest a circuit from Cape Town via Cape Point, Franschhoek/Paarl, the Garden Route, Addo Elephant NP, and then a long run through to Kruger, returning via Blyde River Canyon to Johannesburg. Fly into CPT and out of JHB. That's around 3000 km so about right for 3 weeks. The bit from Addo to Kruger is a two day run, without much stopping, so if that's not of interest, I suggest a Cape Town to Cape Town trip, as above but from Addo returning via Oudtshoorn, and spending more time on the coast and back around Cape Town. Although you'd miss Kruger there are lots of game reserves along the south coast and you'd be able to pick one, I'm sure.

I see this differently. South Africa is a very easy place to travel independently, you can book accommodation easily on sites like booking.com, guidance on the web is plentiful and, aside from any cost savings, it is just so much better than being stuck to someone else’s itinerary (if i am perceiving what a package tour looks like now correctly).

Quite right. South Africa is easy to travel, even for first-timers. Everybody speaks English, the tourist infrastructure is very good - even in more remote places. IMHO the best site for accommodation is the South African web site:
safarinow.com Just check it out.

__________________
Only when we pause to wonder
do we go beyond the limits of our little lives.
(Rod McKuen)