Hengifoss waterfall is on the supposedly not so touristy east side of Iceland. Unfortunately, there are still a lot of tourists here. Luckily, you can have the best view of the waterfall all to yourself which is the view from the top onto the waterfall. Normally, people only hike to the bottom of the gorge.
To get a picture like the one on this pin proceed with caution at your own risk: there is no premade hiking path to the top but when you reach the point indicated on the picture you need to leave the normal pathway onto the grass and hike your way up the grassfield and rocks. Be careful, some ground is not stable and can move any time.
If this sounds too much, then just hike to the bottom of the gorge. Theparking here is paid at a machine.