Iceland during Christmas with toddler and 6 year old.

Not sure about itinerary... driving in the winter I have read can be difficult, so for that reason I feel like I might opt for tours. But someone who has been in winter can comment (we went in June-July). But be aware, it is SUPER EXPENSIVE in Iceland. EVERYTHING is expensive... I live in San Francisco, one of the most expensive cities in the country, and I found Iceland shockingly expensive!

If you take tours, your kids might go for free, so that might be helpful. But food is expensive... example, a subway sandwich (sandwich only) is $15. Your kids are small so maybe really only paying for 2 people, so slightly better, but do research tours, food and see how it is before you go.

The weather can be a big player, it was really wet and rainy while we were there. We still saw the sights on golden circle and south coast, but not as picturesque as it could have been.

Reykjavik has lots of museums, we didn't end up going to too many, but even our older kids were free in many. We really liked the National Museum of Iceland. We had plans for more, but our teen boys were being difficult, so we mostly left them at our house and my husband and I bar hopped and watched the World Cup! :)

Have a fun trip!
Kim

Check out the I Heart Reyklavik website for tours. They have their own tours and recommended partner tours.

I would add that if you are going to rent a car to get all the insurance coverage offered.

You realize at that time of year daylight is only a bit over 4 hours per day.

https://www.timeanddate.com/sun/iceland/reykjavik?month=12

And the daytime high will be below freezing

https://www.timeanddate.com/weather/iceland/reykjavik/historic?month=12&year=2017