Pair Nauthúsagil with nearby waterfall and volcano-context stops only when the day has enough room for slower movement.
The strongest pairing is Seljalandsfoss first, because it is the major South Coast anchor in this area. Gljúfrabúi then gives a shorter enclosed waterfall contrast, while Nauthúsagil adds a more physical ravine version of the same idea. Doing all three can work, but only if you are not racing the rest of the day.
Skógafoss sits farther east in the same route rhythm and usually deserves clearer priority on a first trip. If you are building a 5-day Iceland itinerary, Nauthúsagil should be one of the first things removed when weather, daylight, or fatigue starts pressing the plan.
For a slower area day, Eyjafjallajökull and Gígjökull add volcano and glacier context around the same mountain system. For a wider South Coast Road Trip, keep Nauthúsagil as a flexible active stop before the day shifts toward Reynisfjara and Vík.