The Elberadweg is one of Germany's classic long-distance cycle routes, and its Dresden stretch is especially rewarding. It follows the Elbe past meadows, bridges, villas, beer gardens, and the old city skyline, making it one of the easiest ways to understand Dresden's relationship with the river.
You do not need to ride the entire route for it to be useful. Rent a bike for a few hours and follow the water east toward the castles and vineyards or west through broader riverside scenery; either direction gives a calmer view of the city than the museum core.