Trailforks for road bikes? Is there an iPhone app like Trailforks but for road bikes? I'd like to see where paved paths (bikes only, no cars) are located.
Google maps will show you paved trials open to bicycles and roads with dedicated bike lanes.

If you are a Strava user, you can use the route creation tool with heatmap turned on. That highlights bicycle trails very effectively.

Ride with GPS has a bicycle trails overlay in its route planner.

Really, any significant paved bicycle trails in a given location will be easy to find with a simple Google search, for instance searching for 'paved bicycle paths washington dc' turns up all the major paths in the area.