If you have to pick one quintessential hiking experience in this country, it might as well be the one that's been dubbed "Iceland's Inca Trail." The traditional Laugavegur Route runs for 55 km from Landmannalaugar (in the Friðland að Fjallabaki Nature Reserve) to Þórsmörk (just northeast of 2010's infamous Eyjafjallajökull volcano), and is considered by many to be one of the most scenic 4-day treks in the world. Why? Well for starters, it shows off a little bit of everything Iceland has to offer: glaciers, hot springs, multi-hued mountains, valleys, plains, rivers, lakes, volcanoes - the works. It also comes complete with well-maintained huts and campsites along the trail, which means that you don't have to worry about lugging 4-days' worth of water with you the entire way. And since the trail has become more and more well worn over the years, it's easily doable without a guide, provided you're no stranger to the rigors, risks and requirements of long-distance trekking.
If there's a down side to Laugavegur, it's the brevity of its season: typically late June to early September. This means you'll want to reserve a spot in the huts/campsite months in advance, as almost everyone will be looking to make the trek during this 2.5 month window. Otherwise, daily pickup and drop-off buses are easily managed to and from Reykjavik, and supplies, while not cheap, are easy to stock up on ahead of time. So if you've got four days and want a hands on experience of everything this wild country can throw at you, check the excellent resources below for more specific info and consider adding this incredible trek to your repertoire.
Note:The traditional north-south 4-day itinerary is as follows: (1) Landmannalaugar to Hrafntinnusker Hut (2) Hrafntinnusker Hut to Alftavatn Hut (3) Alftavatn Hut to Emstrur-Botnar Hut (4) Emstrur-Botnar Hut to Þórsmörk. Alftavatn Hut shown on map.