Fjaðrárgljúfur is the big scenic punch near Kirkjubæjarklaustur: a narrow canyon with a river curling between steep, mossy walls. It is short enough for a stop on the Ring Road, but strong enough to justify using Klaustur as a base.
The path can be fragile after wet weather and during thaw, so check signs and closures before setting out. If it is open, stay on the marked trail; the view is good without stepping onto damaged edges.