This park is only a 10 minute or so drive outside of the center of Reykjavik. If you rent a car, it's a cinch to get to, and there's plenty to do. Besides nature trails and bike paths, there's a rushing river that runs through the park, with parts where you can climb to the middle and sit for a while, listening to the gush. We brought a six-pack of the local beer, Gull, and hung out on the mossy river bank on a blanket, listening to music. It was a great place to chill, away from any people or crowds; you feel like you have the park to yourself.