South Coast of Iceland is truely amazing. Several waterfalls, Black Sand Beaches, Glaciers, Volcanos (hopefully not erupting) are all things that you can expect from travelling in the South.
If you are driving yourself and depart from Reykjavik you drive route 1 through Hveragerði (might want to stop there for a hike in Reykjadalur), Selfoss and make your first stop at Seljalandsfoss Waterfall. There you have the chance to walk behind the waterfall. Equally (or almost as) impressive waterfall in a 500m walking distance is Gljúfrabúi a hidden waterfall.
After that you drive the same road to Skógarfoss and in good condition do a short hike to Kvernufoss.
From Skógarfoss you drive towards Vík and stop at Reynisfjara, Dyrhólaey and have a look at Reynisdrangar.
Driving further along the coast your next stop should be Fjarðárgljúfur and after that Skaftafell.
Skaftafell (part of Vatnajökull National Park) is a must stop and please spend some time there. Absolutelly amazing place for hiking and enjoying Iceland´s beautiful nature. Here is a list of Skaftafell´s hiking routes. From there it is possible to do the amazing Glacier Explorer or Glacier Wonders hike and during winter the Into the Glacier in Vatnajökull (do not mistake it for the man-made Into the Glacier tour in Langjökull).
Even further along the South Coast you find Jökulsárlón - The Glacier Lagoon. You can purchase your open ticket to their Amphibian Boat Tour or a time reservation on their Zodiac Boat Tour. During the summer monts (june-sept) it is possible to do Glacier Kayak Adventure Tour on Heinaberg Glacier Lagoon and the meeting point is 40km east from the more recognized Jökulsárlón.