Reykjavik has a wide choice of hotels for family holidays on all budgets. For self-catering, try Luna Hotel Apartments with its well-equipped flats, some sleeping up to 8 people.
As for the rest of the country, some of the enticing options for families are the 150 farmhouses, cottages and rooms in country hotels let by Hey Iceland (heyiceland.is) – your hosts are often real-life farmers, and in some cases kids help look after the animals. Some places also offer extras such as activity programs for children or glacier tours. It’s possible to hire a car and tour Iceland by hopping from farm to farm.
Also worth singling out, 20mins from Reykjavik, is the Viking-themed hotel (and restaurant) Fjörukráin (fjorukrain.is), which, in July, is the focal point for the Hafnarfjördur International Viking Festival, with reconstructions, parades, horse shows, sports contests, and traditional food and drink. But you can stay in this former blacksmith’s workshop all year round, and enjoy traditional feasts served by costumed staff.