Iceland is surprisingly big - you would need a week to drive around the island and take in the sights. Two days will not get you far out of Reykjavik, so you will need to be selective. If you can squeeze in two nights away, I suggest that you consider Landmannalagur (
http://wikitravel.org/en/Landmannalaugar) which is an interesting and colorful geothermal area in the highlands a few hours drive out of Reykjavik. The are a few half day hikes there that are quite spectacular, as well as longer hikes - you will need a full day there to take it all in. The way to get there is from the north (road F208). It is a rough gravel road accessible only by 4WD vehicles, but is scenic. I would be happy to provide accommodation suggestions if appropriate. A trip to Landmannalagur will let you experience rural Iceland, the remote highlands, a geothermal region and the beautiful rhyolite mountains there.
Late September/early October is a good time to go, as the crowds of tourists and backpackers will mostly have gone, prices are cheaper and the autumn colours are at their best. However, the highland roads start to close from then on as snow drifts start to build. Rent a 4WD so you can get off the beaten track (and on the the highland "F" roads). Iceland can be very windy and wet, and areas like Landmannalagur can be very dusty (volcanic ash), so take plenty of lens cleaning gear. And keep up to date with the weather forecasts.
