We did 2 weeks in Iceland with our family of five. 2 adults (30-somethings) and 3 kids (7, 4, and 6months).
We stayed places where we could cook and could sleep up to 4. I would recommend every one of these places, so I thought I'd share with the good folks here:
Reykjavik Central Apartments:
https://www.booking.com/hotel/is/reykjavik-apartments.html
Eidhus Apartments:
https://www.hotels.com/ho731032544/ei-hus-apartments-eyja-og-miklaholtshreppur-iceland/
Hotel Anna (from RS guidebook):
https://www.hotelanna.is/
Skyrhusid (from RS guidebook):
https://skyrhusid.is/
Sol Apartments:
https://www.booking.com/hotel/is/sol-apartment.html
This is a rough version of our itinerary. Traveling without kids, you could do twice this much easily.
Day 1 we did some napping, our test results came back by noon and we picked up groceries. We were too wiped out to do anything, no sight seeing.
Day 2 we did the RS Reykjavik walk, grabbed some famous hot dogs, did a Puffin watching tour (booked through adventures.com) and went to the Whales of Iceland exhibit (got a discount through the puffin tour we booked) kids enjoyed it all, though they complained a bit about the walking around town, got a bit bored with my reading from the guidebook.
Day 3 Golden Circle: 1st stop Thingvellir (I think we got there by 10:30 or so) followed by Laugarvatn Fontana, where we did the rye bread tasting (my kids liked the tour but not the bread) and swimming in the spa (which they LOVED) we did the 2:30 bread tour, headed to the pool around 3, and we finally left for dinner around 6:30 or 7. We went to Efstidalur II for burgers and ice cream, then finished the day at Geysir and Gulfoss. Made it back to the apartment by 11.
Day 4 Fagradalsfjall volcano hike. We did trail A (which is now closed) so it was super cool and a good hike (a bit hard for kids) but none of my expertise will benefit anyone except this: download the parka.is app and pay to park before you get there. The website frequently doesn't work, no matter what credit card you use, but the app is easy.
Day 5 our rainy laundry/recovery day after a big hike. We did the Perlan museum, adults took turns walking to the flea market during baby's nap, and we went to one of the city pools after dinner.
Day 6 check out, walk to a playground in Reykjavik, drive to Borgarnes and eat lunch at the settlement center restaurant. Drive to accomodations in Snaefellsnes. Visit Raudfeldsgja Gorge and Ystri Tunga beach.
Day 7 Arnarstapi to Hellnar hike (got hot chocolate at fjoruhusid), Gestastofa visitors center, Saxholl crater, Kirkufellsfoss, and a few other assorted stops for photos.
Day 8 check out, get gas, get baked goods as Geirabakari on our way back through Borgarnes, head to the south coast. Hike to Reykjadalur to swim in the river. Absolutely awesome! Though one kid did fall in the river fully clothed at the end 🙄. He wore my coat and gloves and had to ride on dad's shoulders on the hike back. Check into our south coast home.
Day 9 Dyrholaey, Reynisfjara, lunch at Soup Company in Vik. Seljalandsfoss and Gljufrabui.
Day 10 Westman Islands day trip: RS walking tour, volcano museum, Sealife Trust, and our overlooked favorite: right at the harbor a statue of a fisherman Asi i Bae. He wrote songs (mostly about the sea and such) and the bench next to the statue has a button you can press to play some of his songs. This delights me for some reason.
Day 11 check out Skogafoss and Skogar Museum. Drive up the coast to Katla visitors center and do short geology walk. Drive to Skyrhusid.
Day 12 diamond beach, boat tour of Jokulsarlon, lunch at cafe at Fjallsarlon, quick walk to view glacier. The long drive back to Keflavik.
Day 13 pack up, get our nose swabs (we did the rapid tests), and have our plan to visit reykjanesfolkvangur foiled by road closure. If I'd been smart we'd have just gone to the pool. Instead we visited Kerid crater. Final dinner at Ingolfskalli.