I loved taking a road trip through this region (useful when heading from Johannesburg to the Cape): long, straight roads, a sky of brass, ochre dust, cacti and ostrich and sheep farms everywhere. And not a tourist to be seen!
The scenery isn't incredible, and can be quite flat and monotonous, but in the mountainous regions and in the parks, such as Karoo national park, there are fabulous views; you'd think you were in an African Wild West. But I preferred the Little Karoo to the Big Karoo; the views are more varied.
In the region, you can stop off at Craddock or Victoria West for the Big Karoo, and Oudtshoorm for the Little Karoo. Incidentally, the gastronomy here happens to be among the best in the country: a stew of Karoo sheep and thyme is served in all the restaurants in the area and, when coupled with some good wine, it's delicious!