If the parking lot is full when you arrive, the reason is rarely the falls. The reason is the Niobrara River, which most of Nebraska treats as the state's flagship summer destination. The Niobrara National Scenic River, designated by Congress in 1991, is a 76-mile reach from below the Borman Bridge near Valentine to the Highway 137 bridge east of Norden. The river is shallow, warm-bottomed, and slow enough to tube without much skill, which has produced a tubing economy that operates more or less continuously from Memorial Day to Labor Day.
Smith Falls is one of the most popular put-in or take-out points on the upper reach. Outfitters in Valentine, including Sunny Brook Camp, Little Outlaw, Graham Canoe Outfitters, and several smaller operators, run shuttle vans and rent tubes, canoes, and kayaks for trips that range from a 3-mile float (Cornell Bridge to Smith Falls, about 2 hours) to a 12-mile float (Sunny Brook to the Berry Bridge, about 6 hours). Expect to pay roughly $20 to $35 per person for a half-day trip with shuttle, more for longer trips and for canoes.
The practical implication for falls-first visitors: arrive before 10 a.m. on summer weekends if you want a calm photo, and try a weekday in early June or after Labor Day if you can. The river is gorgeous and you should consider tubing it, but the parking lot character of the park changes substantially between sunrise and noon on a hot July Saturday.