Aurora Borealis (or Northern Lights) is one of the most spectacular natural phenomena in the world. They are basically green (most times but not always) lights that seem to be dancing in waves in the sky, and can be commonly seen in the far north such as Iceland.
It can be usually observed in dark, clear skies, so the winter season is always the perfect time to go to Reykjavik in Iceland and immerse yourself in their beauty.
However, if you want to go to someplace new but not too far away from Reykjavik, there are other places to choose from as well.
In the neighborhood of Grafarholt, REYNISVATN is a small lake located way within the city limits. It's a secluded place but still quite close to the city, so if you want to see the Northern Lights alone then this is the perfect place.
If you don't want to leave the city but still crave the perfect spot to do your Northern Lights hunting, go to ÖSKJUHLíÐ. It's a hill in the center of Reykjavik and a common outdoors area filled with trees. It's just well within walking distance so you won't have any problem getting back to your hotel after your sightings.
GRóTTA LIGHTHOUSE one of the popular places to go to to see the Northern Lights. This is a well-kept lighthouse in Reykjavik, a usual 1-hour walk from the shoreline after you take the bus #11 to Lindargotu Road. The place is not well-lit; it's facing the ocean, and the overall vibe makes experiencing the Northen Lights in this place even more magical.
BORGARHOLT (KóPAVOGUR) is one of the youngest towns in Iceland. Although there's not much historical significance, you'll get an unparalleled view of the city, and the Northern Lights as well. If you ask some locals within the area, they'll probably tell you about the church on top of the hill that they think is legendary; they call it Mcdonald's Church.
Aside from these places there are still other activities to do to catch the Northern Lights. Numerous agencies are situated in Reykjavik and they're more than willing to help you choose the best spot to enjoy the Aurora Borealis.
Just make sure you come between the months of November and February to make sure you experience this ethereal sight.