I did a stopover in Reykjavik earlier this summer with my sister and 12yoa son. We stayed three nights ($525 for a studio with double bed and sleeper sofa). It was enough to do the Golden Circle and see the city. With another day or two, there are some other day trips you can add. We skipped the Blue Lagoon in favor of the local swimming pool, which was full of families. We had an AirBnB very near the big church, so we were able to eat most of our meals at home. The ones we ate out were budget--sandwiches from the shop at one of the parks, soup and bread in the food hall, etc. Do your beer research ahead and buy the max at the duty free on the way out of the airport. That was a tip I missed and wished I had known about.
We also went to Oslo, Bergen, Aarhus and Copenhagen. We had free accommodation in the latter two (yay!), but we did alright with AirBnB in Oslo, which is pretty easy to get around. We stayed there three nights ($240/1BR w/sleeper sofa). I had been before and couldn't wait to get back to the Vigeland sculpture park, so we stayed in that area (Frogner). My son liked roaming the waterfront area, which has gorgeous modern architecture. We also hit up the maritime sites out on Bygdoy (except not the Kon Tiki). We really liked the Fram. We took the bus out there. We ended up stopping at the open-air folk museum, which we also really enjoyed.
We were supposed to do the Norway in a Nutshell, but I screwed that up. You can do it yourself and save a little dough, but you have to reserve everything ahead. For whatever reason, I didn't think I could, so I didn't. We ended up going to Bergen a day early and staying at an overpriced hotel. But that town was pretty great. We loved Floyen, especially. Also in between Oslo and Bergen, there was a place where loads of people got off the train with their bikes (or, maybe, rented them?) and biked down to another train station. I don't remember the details, but if that's something you're into, you should definitely check it out if you're going that way.
From Bergen, we took the overnight ferry to Hirtshals in Denmark. My kid's been on a bunch of cruises, but he really liked his bunk bed. Hirtshals has a ho-hum aquarium and surprisingly bad connections to the rest of Denmark, and the one-way car rental fee from there is a scandal. There are also ferries from Oslo to Copenhagen, but I feel like if you're going to Sweden, the ferry doesn't make sense for you.
Aarhus is very family friendly. We enjoyed the roof deck of the department store (whose name I forgot), DOKK1 (coolest parking garage EVER), the art museum's rainbow tunnel, the infinity bridge (where we swam because it was so f-ing hot this summer), the Viking Moot (not sure that will be in Aarhus next year), the museum with the bog man, and their mini Tivoli. We made a day trip to Legoland, but I wish we'd gone to see the Lego House, which is unique.
The highlight of our visit to Copenhagen was hunting for Thomas Dambo's Giants. We were aided greatly by Oregon Girl Around the World, a blogger who has two posts that provide great information about how to find the sculptures. With a car, we were able to do all in one day. Really, this is a must-see for this age group. We had 12, 11 and 9, all boys, and they had a great time, as did the parents. We packed a picnic lunch. It was a great day.
In all three countries, everything was expensive, although I think we paid less for our Iceland AirBnB than we did in Amsterdam. We ate in almost exclusively, which helped, but even groceries were expensive. In Aarhus, we did much better at the farmer's market. We had great pizza in Oslo, and it was very reasonable. Even at home, we do a meal we call "snacks"--a mix of healthy and not, special drinks for everyone. Works very well for travel. We tried a lot of weird chips.
Skyscanner is good for pricing flights. It lets you search by the month.
