A couple of weekends ago, my wife and I took the bikes down to the New River Trail, where we picked it up in the Draper area.
The New River Trail is an abandoned railroad right-of-way, part of the Rails to Trails Program, and parallels the New River and Claytor Lake for 39 miles. The entire park is actually 57 continuous miles long, and heads through Grayson, Carroll, Wythe and Pulaski counties. Here's a map.
If you're looking for a new bike ride that's just gorgeous, I'd encourage you to check this one out.