Sacrifice a goat every day to please weather and sun gods.
In the middle of the winter it is mostly overcast, and when it is not, sun needs to be extra active (which is pure luck)

Two years ago i spent 10 nights looking at the sky in iceland, willing to drive to any place where the sky was clear - no luck.

what >>1060557 said, sacrifice animals for some good weather both to see aurora borealis AND to be able to travel around a bit

since 4 days is not that much, I'd recommend renting a car to see the waterfalls in the south, going to Dyrholaey and Vík, maybe getting to Snaefellsness Peninsula too, which is pretty and close to Reykjavik

i'm going to iceland too next year, around the same time. any recommendation on local tour?

>>1060548
I saw the Aurora really nicely while I was there in a late August/early September trip I did (not even peak season), and they were visible right in Reykjavik while walking on Laugaveger St and down to the opera house, everyone was looking up, though dimmer from city lights than I saw them from the roof of my hotel in Budir, and again in Selfoss, and really you can see them everywhere and in between, so don't think you have to drive too far away. The darkest skies for it, imho was Budir though. but I have no idea how accessible roads are in January, and if can drive the ring road or need some snorkel-geared special SUV (reason for a tour). Just pay someone to take a tour, and they will cancel you if the odds are bad and move your night. It's down to a science now with the predictions.

http://www.northernlightsiceland.com/northern-lights-forecast/

>>1060548
>also some unique experience of iceland
>>1061018
>any recommendation on local tour?
Something very unique I did was visit Snorrastofa. Sit in snorri's pool where Gorbachev and Reagan signed a peace treaty or something, but if you're into literature (and you should do a little intense study before you go to Iceland), it really comes alive to see where other people go to study medieval lit.
http://www.snorrastofa.is/vidburdir/
The vicar/rectory guy there and his wife are amazing historians and very congenial. Reykholt has 2 natural wonders closeby too. Hraunfosser is lovely, and there's some hot springs that is worth a stop near the hekla river (cave tours if you're really adventurous).

Now, on the way, there's a odd little museum in Bogarnes with hard-to-describe but tasteful and well-done artistic dioramas that narrate stages of the tours and ipod narration as you walk (2 choices for the tour subjects) the settlement and early vikings in Egil's saga, with a nice handicraft gift shop and great little restaurant. Within Reykjavik, ehh, the church is a quick view but boring inside because it's so stark and undecorated, volcano move museum (ehh, can netflix stuff instead). Shop, dine, drink, and enjoy the architecture. That's about it. There's some malls and strip shopping further out in the suburbs. Might like some kitchy viking night meal in Hafnarfjordur (just a few minutes south of Reykjavik). http://fjorukrain.is/en/about-the-festival/
Medieval Times kind of meal atmosphere with high prices, hotel attached has a cave bar and a pretty decent hot tub and little rock garden spa area for hotel guests....like most rooms in Iceland, think spartan IKEA furnished with less gloss or cheer.

>>1061077
>odd little museum in Bogarnes
Forgot the link. It's actually called the Settlement Museum.
http://safnabokin.is/museum/the-settlement-centre-in-borgarnes/

In the unseasonably warm Autumn, and still nice weather that I was there, it wasn't even a 45 min drive out of the city to Bogarnes, and you do a cool tunnel that makes your ears pop from the depth. " A tunnel under a fjord, the Hvalfjörður Tunnel, is among the longest underwater road tunnels in the world, and goes as deep as 165 m (541 ft) below sea level.[1]"
https://en.wikipedia.org/wiki/List_of_tunnels_in_Iceland

Depends on what kind of traveller you are, but when I was hitchhiking the ring road I met a lot of tourists who turned out to barely have experienced the country. They were just driving around in their car stopping for a photo now and then. Meeting (and driving) with people who were actually from Iceland was one of the most interesting parts for me because they could just tell you a lot more about the country, history, changes, everything. Try to get in contct with locals more than just at the car rental or hotel is my advice. Also expect some cold-ass weather between Jan and Feb.

If you're renting a car, get a car with spiked tires. And insurance! check road.is religiously.

And you're not on some sort of adventure. People live here and you have to treat your environment with respect.