Located 85 mi/135 km southeast of Maseru, Sehlabathebe National Park in Lesotho has some wild animals, but it's primarily a place to escape and unwind. There's a rustic lodge and plenty of space for camping (take everything with you).
Sehlabathebe can be reached by air, via a decent dirt road (in a four-wheel-drive vehicle) from Maseru or by hiking in from South Africa over the Drakensberg escarpment.
