The Northern Lights can be elusive and unpredictable: you need the right combination of season, weather (clear skies on cold nights), location (away from city lights), length of stay (the aurora borealis occurs in cycles of sightings over a couple of days followed by 4-5 nights of inactivity) and just plain luck. Track sites like www.northernlightsiceland.com and www.agust.net/aurora to improve your chances, and consider taking a bus tour to the well-regarded Reykjavik Excursions (www.re.is/day-tours/northern-lights-tour). Driving about would be the best way to see the wonders of Iceland but the roads can be treacherously sleety in the winters, even for locals. Follow the guidelines at www.safetravel.is.
This classic driving itinerary (though eight days may be too little!) will take you from Reykjavik, after you are suitably rested, for the road to Borgarfjordur, stopping for the Hraunfossar (water flows out of lava into the river below) and the Deildartunguhver hot spring. Continue up the picturesque meadows of the Skagafjörður Valley to Akureyri, where you can halt for a couple of nights to explore the splendid Myvatn lake area (for the legendary volcanic wonders of Dimmuborgir, Skútustaðir, Krafla and Námskard, extraordinary walking trails and rare bird life, with a stop at the Godafoss falls along the way). Head next for the Ásbyrgi gorge via the coastal Tjörnes peninsula to the moonscapes of the Möðrudalur highlands till you halt at Egilsstadir in the Hérað valley. Then follow the Ring Road no. 1 to explore the East Fjords along the scenic old coastal route to reach Höfn (tough mountain driving today). Onward then past Europe’s largest ice cap to the glacial lagoon of Jökulsárlón at the foot of the pyramidal peak of Hvannadalshnúkur—walk along the banks of this breathtaking vista, or take a boat trip to see breaking icebergs up close. You will cross the black sand plains of Skeiðarársandur and the lava field of Eldhraun to reach Vík, where you can stay before your last leg of driving past the stunning Skógafoss and Seljalandsfoss waterfalls, thence to the hugely famous Geysir springs and Gullfoss falls, past the Laugarvatn lake back to Reykjavik, which I will leave you to discover for yourself. You will love the Northern Lights when you see them, but there is so much else that will take your breath away, too.