If you want a long, flat, off-road run in the Sun Valley area, the Wood River Trails are a good option. Also known as the ‘bike path’, the Wood River trail is a paved, multi-use path that runs for 20 miles. The trail starts just north of Sun Valley, and parallels State Highway 75 through Ketchum, Gimlet, and Hailey, ending in Bellevue. Fairly open, with good mountain views.
There are some tributary trails and additional options. Additional information here.