There are lots of great options for a safari in South Africa. We're partial to some of the lodges located within the private game reserves adjacent to Krueger National Park.
You could, of course, do a self-guided driving safari within Krueger National Park itself, but that's kind of limiting, because while driving through the park you have to keep your vehicle on the road at all times. So, you're limited to seeing only those animals that are near or on the road. Plus, you don't have the benefit of having a trained guide or tracker along with you.
At a safari lodge, you don't have to worry about any of that. The private game reserves share a border with the National Park, but there are no fences. So, animals wander in and out of the park and through the various private reserves.
You'll hear people talk about the "big five"--so named, not because they're the largest animals you'll see on safari, but rather because they're the ones that are the most dangerous to hunt on foot. These five animals--lions, leopards, elephants, rhinos and Cape buffalo--can all be found in the private reserves surrounding Krueger, but no lodge will be able to guarantee that you'll see all five. I was lucky to see all of the big five on my first safari, in the Timbavati reserve, but on my next safari in Sabi Sands, the lions and leopards eluded us--even though Sabi Sands is renowned for the likelihood of spotting leopards (the most elusive of the "big five"). But you'll assuredly see lots of other animals, beyond the "big five." On my first game drive, I was flipping out over impala, springbok and other antelopes. And by the end of the trip, I was like, "Fine. It's another herd of antelope. Let's move on." Zebra, giraffe, warthogs, hyenas--they're all out there, and with the help of a guide and a tracker, you can probably find most of them!
Here's a typical day: Get up before sunrise and hop in a open-air Land Rover with your guide and tracker. Head out into the bush looking for wildlife. Stop at sunrise in a clearing for coffee and rusks (think: South African Biscotti), then back in the jeep to look for more wildlife. After a little bit, head back to camp for a full breakfast, and maybe a nap. Many camps have a swimming pool, so after lunch, you could go for a dip, though one time an elephant wandered into our camp to drink from the swimming pool, so we had to quickly run for cover! Many lodges and bush camps have verandas overlooking watering holes or rivers, so during the heat of the day, before and after lunch, you can just hang out and watch the different animals come to get a drink. In the afternoon, it's another game drive, stopping at sunset for "sundowners"--cocktails at sundown in the bush. Very civilized. Then your game drive continues after dark, where the tracker looks for some of the nocturnal animals by shining a spotlight into the bush, and looking for the reflection of their eyes. After a while, you'll return to your bush camp for dinner, and maybe hanging out around a campfire with the staff and other guests. Then, off to bed--a staff person might have to escort you to your hut or tent, in case there are animals lurking about--so that you can get up the next day and do it all over again.
For the safari portion of your trip to South Africa, three days seems about right. There are accommodations to fit every budget and style. Tented camps, luxury tented camps, reed rondavels with thatched roofs, small bungalows, or larger lodges--you can definitely find a safari experience that'll ensure that you're comfortable, while having the full experience of being in the middle of the African bush. Since the experience is pretty much all-inclusive, so you'll get three square meals a day, and all of your game drives are included.