One of the most spectacular natural phenomenas in Iceland are the northern lights. Due to its sparse population there is, apart from the larger cities like Reykjavík, little to no light pollution which makes it ideal to see the lights. In and around Egilsstadir there are many places to observe the northern lights only on a short distance from town without being disturbed. For instance the road up hill to Seydisfjordur has several parking spots to stop safely. Also close to Vök Baths at Urridavatn is a good spot to see the lights.
Note: Best chances to enjoy the northern lights are from Mid September to the end of March. The northern lights are best visible with a clear dark sky. Check the weather and aurora forecasts to assure yourself about the chances to see the northern lights and be safe.