You don't have to go far from Reykjavík to find wonderful areas for walking among trees (well... WE call it trees!) and wild flowers to the music of birds. Heiðmörk is such a place and one of my own favorite places for walking.
It can be approached from different directions but the most direct way is to take the main road from Reykjavík, Suðurlandsvegur (Road 1), as if you were going to Hveragerði or Selfoss.
After you have passed a small lake, Rauðavatn, in front of the last buildings to be seen in Reykjavík, look out for a sign on your right, Heiðmerkurvegur nr. 408. Turn there, drive on, passing the "red hills" called Rauðhólar until you find an area you like. There are many walking trails. Just take care not to get lost...
You could also make a stop near Rauðhólar (lava hills) and walk there.
