Ride Routes
Like most aspects of Scouts BSA and Venturing, Cycling Merit Badge should be "youth-led." Scouts taking this merit badge certainly should pick the routes they want to ride so long as they keep in mind safety and feasibility.
Detailed Ride Options
The links in items 1 to 5, below, lead to detailed maps and ride descriptions that could be feasible for riders based in Northern Virginia.
The rides in Part 4 and 5 exceed the requirements of the Cycling Merit Badge. They are provided because Camping Merit Badge has a requirement go on a camping trip that includes a "bike trip of at least 15 miles or at least four hours." See Camping MB, Req. 9(b)(3).
Maps to Plan Your Own Local Trips
There are lots of great bike trails and bike routes in our area, and several website have the details:
Fairfax County has an interactive bicycle map of the county;
The Capital Trails Coalition has a website full of trails.
"Bike Washington" is an older website, but it still has lots of great information;
Maps and Information for the Mid-Atlantic States
If you have the transportation support, and a real spirit of adventure, try these links: