For this stay, we chose to stay in a cabin via Airbnb. We wanted to stay out of the towns (for better chances of seeing the Northern lights), but also we really like to do our own food and for the kids to have some room to play around without disturbing other guests.
Tip: There are so many great airbnbs in this area. However, Lofoten is huge and you often drive a very long way to go see the sights, hike or do grocery shopping, so be aware of the distances of the sights you wish to visit, when you book your accommodation.
For other accommodations I can recommend:
Nusfjord Arctic Resort on the rorbows of Nusfjord. Amazing location in the secluded fishing village Nusfjord and such a perfect small resort: https://nusfjordarcticresort.com
Also, Trevarefabrikken in Henningsvær is super nice: https://www.trevarefabrikken.no/
Want to try to live in light house? There is the perfect spot in Lofoten. Although, I would probably only go here during the summer time: https://www.littleislandlighthouse.com
There is free camping in Norway, and I think this van option is brilliant (also a summer vacation option): https://www.lofotenvanlife.no/
Lastly, but not least, this is my total dream location. We had it all booked for out stay in March, however, it is 3-4 hours north of Bodø, and for a trip of 4 days, it was just too many hours of transport back and forth to make sense. But maybe one day, when we hopefully go back: https://www.manshausen.no/