The Teton River is an 81.5-mile-long tributary of the Henrys Fork (Wikipedia) that begins in the Teton Basin near Victor. It flows north west towards Rexburg.
The upper river in the basin is easily accessible at several locations, while the section that flows through the famed Teton Canyon is nearly inaccessible.
The lower Teton River is accessible at the Newdale Bridge, the old Teton Dam site, Spring Hollow near Drummond or if your in a pontoon and wearing a life jacket - the slide at Bitch Creek confluence. Make sure your prepared if you decide to descend the Teton as there are many natural hazards besides the river including large lake sections that can strand you on a windy day and rattle snakes on the banks. Stay on your toes!