5. Hiking, Esjan or Ulfarsfell

The 'city mountain' in Reykavik is Esja, some 700 meters high. It is a bit steep, especially the last part, but children over the age of 8 should be able to climb it. It takes about 1 - 2 hours to walk to the top, but of course a half way can often be enough. From the top there is a great view over the city and in good weather you can see pretty far.
Smaller mountain, but still with a great view over Reykjavik and its surroundings is Ulfarsfell, close by.
Close to those mountains there is the house of Halldor Laxnes, the nobel price winner in litterature 1964, and it can be worthwile driving to his house and take a look around.
After the activity a nice swimming is essential. There is a new swimming pool in Mosfellsbaer with many slides and a nice café where you can have refreshment after the swimming.