A lot of hotels have limits for under 18s, but I could find no mention of an age limit on Accor hotels' website.
hostelworld states "Most hostels do not have any age restrictions for guests. Hostels that do restrict guests with a minimum or maximum age limit should have this clearly displayed on their microsites. Normally it is 18-35 years old." A couple of random hostels I looked at did not display such restrictions. I would go for a private room if at all possible in a hostel though, or get enough friends together to occupy a full room.
Flights booked: NWI-AMS-JNB-DUR, JNB-AMS-NWI