Robert Rives posted the route:
The Neuse River Trail, as described on Wikipedia:
"The Neuse River Trail is a 33-mile (53 km) long paved greenway located in the Research Triangle region of North Carolina, running along the banks of the Neuse River from Falls Lake Dam to the town of Clayton. The route passes through the jurisdictions of Raleigh, Wake Forest, Knightdale, and Clayton in Wake and Johnston counties. The Neuse River Greenway trail is part of the Capital Area Greenway system as well as the Mountains-to-Sea Trail that crosses North Carolina from the Great Smoky Mountains to the Outer Banks. Open to both cyclists and pedestrians, the Neuse River Trail is the longest greenway trail in North Carolina and the longest paved trail between northern Virginia and western Georgia."
NRT Website (only has info for Wake County portion): www.raleighnc.gov/parks/content/ParksRec/Articles/Greenways/NeuseRiverTrail.html
The southbound (downhill) route has a Strava segment.