[font color=\'#000000\']I can´t disagree with anything that Michael has said, but in my now lengthy experience of visiting/working/holidaying up there, there is very little need for a 4x4 unless you want to cross the hinterland. I have been on terrible roads, many times, with my company´s Toyota Corolla (a machine I have growing respect for!) so you should do just fine. Just don´t push your luck - it can be a long wait for help if you ground the car.
The south coast, as Michael says, is stunning. As you will not be running short of daylight on your trip (I was there last week - it got dark-ish at about 2300hrs) you can stay out as long as you like before heading back to Reykjavík for metropolitan comforts. Besides, you will find it a bit tricky finding hotel/B&B accomodation anywhere by now.
Go as far as Vík í Myrdal (2 1/2 hours drive) on the south coast and you will get a fairly representative idea of what you will see all along the coast. Amazing black sand beaches, ice caps, sheep, waterfalls bla bla. The glacial lagoon is too far to go on a day trip from Reykjavík - but is unforgettable if attempted.
Go north from Rvk to Stıkkisholmur on the Snæfellsnes peninsula (again, about 2 1/2 hours) for more dramatic scenery, thousands of islands and skerries on Breiğafjörğur (Broad Fjord), extinct volcano, more sheep.
One drive you can do is to go to Landmannalaugar, a hot spring some way into the interior of the country which is in the most astonishing volcanic scenery. The principal route there is fine for a 2WD, except you´ll have to walk the last 200 yards or so where there is a stream to ford. I guess this is 4 hours from Reykjavík, is off the south coast drive so you can combine it with something else. Highly recommended.
Have a good trip,