Reykjadalur (literal translation: ‘Steam Valley’) is one of the easiest hot spring areas to reach from Reykjavík. A short drive (45 minutes) brings you to the town Hveragerði and from there you can hike up to the warm river that flows down Reykjadalur valley.
The hike is not very demanding (although it’s not recommended for people that are afraid of heights since at one point you’ll be hiking along the top of a deep gorge) and you reach the warm river after about 45-90 minutes (depending on how fast you walk and how often you stop to take pictures of the waterfall in the gorge and all the pretty bubbling muddy hot springs on the way). There are no facilities for changing your clothes when you get up there.