I have the luck to work for an Icelandic bank and have spent many months up there over the past 4 years. You have a couple of options from Reykjavík in the limited time available to you:
1. West Central Iceland. The Snæfellsnes peninsula is just over two hours drive north of the capital. Drive around the whole thing. Very dramatic mountain ridge all the way down culminating in the imposing cone of the extinct Snæfell volcano. Some cliffs, seabirds, seals, lava flows, a glacier, dramatic cloud formations (all too often, I´m afraid!). It´s Iceland in miniature and well worth thinking about. Not so heavily visited by tourists either.
2. South Central Iceland. You can take in a lot on this one too. You have to see Thingvellir - seat of the old viking al fresco parliament - very dramatic setting in a volcanic plain (on the mid-Atlantic ridge - Iceland is splitting apart there and there are many chasms and extinct volcanoes to see.) From there, drive on to the very impressive Gullfoss waterfall and Geysir (the original one). Then drive on to the south coast heading east, driving past the first two of the South´s big ice caps, Eyafjallajökull and Myrdalsjökull, and two imposing waterfalls. The vast black sand beach between Dýrhólaey (basalt arch poking into the Atlantic - festooned with puffins often) and the town of Vík is remarkable. Amazing basalt cliff formations at either end. Make sure you get to Þingvellir and Gullfoss/ Geysir early other wise it can get very busy - especially at weekends.
Either of those would do the trick, I reckon.