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From Vienna you can travel east to Slovakia and Hungary or west to Krems and Passau. To get to the boats you need to head to U1 station Vorgartenstrasse and follow the signs to DDSG. You can buy the tickets from the counter there or sometimes from bigger stations. Their internet website provides more information. Most boats run from April to October and there are sometimes special offers in conjunction with trains. There are also themed Danube cruises.
MESSING ABOUT ON THE RIVER:For a trip on the Danube Canal, you can get a boat from the quayside at U1 Schwedenplatz which runs several times a day during summer. For a nice summer afternoon on the river head to U1 Alte Donau or Donauinsel and hire a motorboat or a peddle boat. (prices start at around 10 Euros per hour)
An interesting way is on the hydrofoil which sails daily from Budapest, calling at Bratislava on the way, it's a summer only service.