In the middle of Reykjavík is an oasis called Valley of Elliðár. This outdoor recreation area has rivers, waterfalls, birds, forest and flowers. It's a little retreat for the city people.
This beautiful area is so far virtually unknown to the normal tourists. For a great day of picnic and outdoor activites without ever leaving the city then this might be a good choice.
There is a hectic amount of rabbits surrounding the west of the valley, close to bridge.