The paved Glenwood Canyon Bike & Pedestrian Path follows the winding course of the Colorado River for 16 miles.There are restrooms and picnic sites. Bighorn sheep can be spotted on the canyon walls. The path is closed in winter, and sometimes there are seasonal spring closures due to high water at run-off.
From Basalt to the trailhead: Take Highway 82 to Glenwood Springs. The trail starts just east of the Yampah Spa Hot Springs Vapor Caves.
More here from Aspen Trail Finder.