Congrats on the win!
Pre-covid, we went to Reykjavik at exactly the same time of year. The snow was apparently heavier than usual for Dec, but it was fabulous. We walked everywhere within Reykjavik itself- sun voyager sculpture on the lake, the museum, cathedral, the opera house, main shopping strip etc- don't forget the penis museum! 😆Even walking through the cemetery en-route to the museum was magical and so peaceful and pretty.
They had many well planned day trips from Reykjavik via bus- so we didn't bother hiring a car either. We did the golden circle tour which included the geysir and Gulfoss waterfall. Gulfoss was the most extraordinary waterfall I've ever seen- think of Niagara falls with ice and snow all around it.
We also did a northern lights trip. One thing to note is that what you see from the naked eye- is nothing compared to what the camera will pick up. I was very disappointed to see some wispy, green waves in the sky- until I looked a the camera photos which looked amazing! We used both these companies for our tours. Their main bus depot is in town, otherwise some trips will pick up and drop off from your hotel Gray Line Iceland - Golden Circle Tour
Golden Circle Tours in Iceland | Reykjavik Excursions
There are many, cheaper, hot springs around which are equally lovely, but blue lagoon is the most famous (and most expensive). IMO- its better to do it to/from the airport. We spent a few hours there before our return flight home and it was lovely.
In terms of clothing, I wore salopettes, ski jacket and layers- even during the day. You will see locals in jeans and a jumper and I'm sure they laugh at the tourists in all their ski wear, hats and gloves. There was a focus on locally made and knitted jumpers, beanies, scarves etc and some lovely items in the local craft shops.
The sun didn't come up till about 11am and it set at 2pm! Shops were still open till the evening though and everything carried on as if it was still day time. It was lovely seeing Christmas decorations around and everyone had a candle arch in their windows.
Alcohol is very expensive. Assuming things are still the same, there was a duty free shop within the airport for arrivals, so you could buy alcohol there a bit cheaper than in town.
We stayed at this place https://ok.hotelsreykjavik.net/en/
It was very central, and although we mainly ate out- it did have a kitchenette in the room. There was a supermarket down the road, so it was very handy to be able to reheat things, or make breakfast ourselves (also cheaper!)
We only stayed either 4 or 5 days but had a lovely time. I have no idea what summer is like, but it didn't feel overly crowded or busy when we went. Sorry this has turned into an epic reply- but happy to answer any questions you have.