Hveragerði Public Park is a pleasant green break in the middle of town, with the Varmá River running through it and the small Reykjafoss waterfall tucked into the park. The ruins of an old wool mill add a little local history to what would otherwise be a simple riverside stroll.
There are benches and picnic tables, and paths lead out toward longer walks around the Hveragerði area. It is not the town's headline geothermal sight, but it is an easy place to slow down between hot springs, bakeries, and trailheads.