Danube
The Danube flows through many cities, including four national capitals (shown below in bold), more than any other river in the world. Ordered from the source to the mouth they are:
The Danube is navigable by ocean ships from the Black Sea to Brăila in Romania and by river ships to Kelheim, Bavaria, Germany; smaller craft can navigate further upstream to Ulm, Württemberg, Germany. About 60 of its tributaries are also navigable.
EuroVelo
Running from Saint-Nazaire on the mouth of the River Loire along that river eastward through France, EV6 passes over the border to Switzerland to Lake Constance and then on to Tuttlingen in Germany, where it begins its way down the Danube following the (Danube Cycle Route). It follows that river, Europe's second longest, through Germany, Austria, Slovakia, Hungary, Serbia, Bulgaria and Romania to the river's mouth at the Danube Delta. It then continues southwards to end in Constanța, on the Black Sea.
EV7 runs from the North Cape to Malta, will whisk you from the Arctic Circle in Norway, the land of the midnight sun, to island hopping in the Mediterranean.