The river and the greenway in Gold Hill
Gold Hill lies along a bend of the Rogue River, at about 1,085 feet elevation (Wikipedia).
The Rogue River Greenway
The Rogue River Greenway project describes a 30-mile chain of parks and public access areas along the river, linked by trail between Central Point and Grants Pass. Its website names the City of Gold Hill among the partners, along with Jackson and Josephine counties, the Rogue Valley Council of Governments, Oregon State Parks and the Oregon Department of Transportation. It says over 85 percent of the greenway would be on public lands.
Jackson County's mapping portal also carries a Rogue River Greenway layer. We did not find an official statement of how much of the trail is open in Gold Hill, so check the project website for current progress.
Oregon State Parks says the Rogue River Greenway Trail runs 4 miles through Valley of the Rogue State Park, a short drive from Gold Hill.