Kruger National Park is an easily accessible "safari reserve" located in the eastern half of the country, near the borders of Zimbabwe, Mozambique, and Swaziland. It is also extremely rich in wildlife, and a great starting point for first-time safari-goers, with facilities that put comparable National Parks in the United States to shame. While on my three-day trip there, I saw 4 of the "Big-Five" - lion, leopard, rhino, elephant, and buffalo. The chances of seeing the "Big-Five", especially in the southern part of the reserve, seem to be high.
The schedule for most short organized tours to Kruger, from Johannesburg, is a three-day safari trip, with only one day spent in the park and no overnight accommodations in the park. However, the cheapest of these organized tours was ~$600 USD p.p, which for what is offered (camping accommodation, "private reserve" stays, etc...) I found extraordinarily expensive. A better alternative is to self-drive (rent a car) to the park; indeed, this is what most South Africans do.
To self-drive, you'll need to rent a car in Johannesburg, or rent a car in Nelspruit after finding your way there (either via bus or flight). Given the near-impossible nature of traversing Johannesburg without a car, the former seems to be more viable. See earlier Johannesburg post for details.
You will also need to book accommodation in the park at rest camps (and pay for your conservation fee to guarantee your spot, especially in high seasons). This part can be challenging to do with only few days' notice, but there were a few family cottages and huts available with 1 days' notice in the Southern section of the park for R1375 (for 6 ppl). Despite the capacity restrictions stated on the website, the rest camps are so large that nobody will check to see how many you have per unit; and the cottages can easily sleep double or triple the accommodation capacity. Those with kitchens come fully equipped with pots, pans, silverware, a burner, sinks, fridges, and microwaves. Bookings can be done at www.sanparks.org. Note that if you pay a conservation fee and stay overnight, your conservation fee is still valid the next day; so technically you can stay almost 48hrs on one fee of R180.
Once inside the park, one can also choose between different activities, such as a bush walk, bush barbeque, or night/afternoon drive. They seemed not too popular, and rates vary between rest camps (for the former and latter activities, R200-350). We chose to do the morning bush walk and night drive; although both were moderately interesting, I would not repeat either activity for the price - most of the wildlife we saw was from driving around the park, stopping where others did.
On the way back to Johannesburg, the tours will take you to Blyde River Canyon, easily accessible out of Kruger Gate; if it is cloudy, however, do not go! - you will not see anything.
With a car split among 3, the cost for 3 days including car rental, gas, housing, tours, etc... came out to $350. This included the expensive morning walks and night drives ($100 pp), and fairly expensive housing for 1 day ($100 pp). By using hut accommodation or splitting a cottage among more people and by avoiding the in-park walks and drives, one can do this trip for a mind-boggling $150 pp, which is an amazing cost for an African safari.
A yawning lion - 5-ft away from the photographer