On my upcoming trip I had the option to have long layovers in between flights in Turkey, Qatar, or Abu Dhabi. Qatar and Turkish airways offer free tours of the city if you have a layover of certain length. Qatar is what I booked(cheaper and better quality) and found out I might not qualify for the free tour by not booking directly with them, but you can get visa to enter country for like $27 US then take a taxi to hit tourist areas, get a hotel, or whatever.
Since my flight arrives at 4:40pm and don't leave to head to JoBerg until 2:20am, planning to leave airport and head to the Souq Waqif (open air shopping area with restaurants) and take in the sights. The Islamic Art Museum is right there also to walk to if you want. Taxi shouldn't run more than $35-40 im told in multiple online sites and for me personally, it should be a nice way to be in another country briefly while on layover between flights. My plan is to shop a bit for family, eat, and take it in, then head back to airport and continue flight to Africa.
Check the airlines you are looking to book and most layover in Europe or Middle East (delta had straight from Atlanta to S.A.), but saw layovers in Zurich, Paris, London, Madrid, Amsterdam, Qatar, Abu Dhabi, Turkey, Dubai..... If you aren't traveling with gun or bow, shouldn't be an issue and why not take in some sight seeing in a foreign country while on way to hunt Africa?