The Arethusa Falls Trail is 2.6 miles out and back with about 900 feet of elevation gain, almost all of it on the way to the falls. From the US-302 trailhead the route climbs gradually through hardwood and then hemlock forest, crossing several drainages on small log bridges, and gets steeper in the last quarter mile before delivering you to a large granite viewing rock at the base of the falls.
It is a real hike, not a roadside stop. The grade averages about 700 feet per mile on the steeper second half, which is moderate by White Mountain standards but enough to slow children under about eight and adults who are not used to hill climbing. The tread is mostly rocks and roots, with no scrambling and no exposure. Trail runners and athletic kids handle it in about 90 minutes round trip; an average pace is two and a half to three hours, including time at the falls.
The optional Bemis Brook Trail spur on the lower section adds about 0.3 mi and visits Bemis Falls, Coliseum Falls, and Fawn Pool before rejoining the main trail. It is worth the extra time in moderate-flow conditions; skip it in high water because the brook crossings flood. Many parties take it on the way down for the gentler grade.
For families with older kids who are used to walking, Arethusa is doable; for families with young children, the Diana's Baths trail (also White Mountain National Forest, ten minutes by car each way and 80 feet of total gain) is the better choice. See our Diana's Baths guide for the comparison.