Iceland Air lets you do up to a 7 day stopover to Europe then you can fly straight home. We arrived late afternoon, had a full day there, then left the next morning. Not ideal, but all we could do with school finals, etc. We did a south coast guided tour with Goecco, and did family pictures with Mink photography. We stayed at Reykjavik Residence Hotel, which has regular rooms and full on apartments. There were 8 of us total, our family of 6 and 2 grandparents. We had a great 3 bedroom apartment. It's one street off the main street, so quieter than main street, and centrally located. The service is great and you can get breakfast delivered to your room for $10/day/person which is actually enough food for breakfast and a decent lunch, and includes a fresh loaf (or two) of bread.
Iceland is getting busy during tourist season. If you are interested in stopping over there, make hotel reservations by early spring at the latest to get your first pick. Iceland is also cracking down on unlicensed airbnb's so there are fewer of those available now.
I loved Iceland so much I went back with my friend in March. We did a two day overnight tour to Jokulsarlon glacier lagoon with Goecco (which included lodging and dinner that night), and a day at the Blue Lagoon. It was, again, awesome.
We stayed at the Scandic Palace in Copenhagen, which is at the foot of the central pedestrian zone and across from Tivoli. The rooms were very nice and huge by even American standards. We did the free walking tour, which gave us a good lay of the land, then just did our own thing after that. We saw the Paris Opera House Ballet premier Copellia at the Royal Opera House there, sitting about 10 rows behind the Queen. We spent a day at Tivoli, which the kids loved.
Some Viking portraits:
