Rain or shine, when Icelanders have a free hour, they go to the pool. Head straight for your local swimming pool and spend a half-hour doing laps or just stretching out in the hot tub, watching children play, teenagers flirt, and old men gossip. Don't worry if it's raining -- Icelanders will still be at the pool.
If the weather's nice, you're never far from nature in Iceland. Just walk to the edge of town and keep going (or, in Reykjavík, walk along the waterfront.) Enjoy how lightly Icelanders live on the land, and how close they are to the stunning beauty that surrounds them.
If the weather's lousy (and it often is), take advantage of Iceland's coffee shop culture. If you're in Reykjavík, settle into one of the cozy coffee shops along Laugavegur or Hverfisgata with a friend or a book you picked up at Mal og Menning. If you feel antsy, pick up a one-day Reykjavík Card at a tourist information office for ISK 1100, and use public buses to do some museum-hopping.