Only 12 km away from Bratislava downtown (majority on cycling path) you can visit remains of Devin castle at the confluence of Danube and Morava. You would not be allowed to enter into this area before 1989 because of the Iron Curtain border, but today this is a nice place for biking and observing nature. You can use the newly built cycling Bridge of the Freedom to visit Austria behind Morava river and Schloss Hof castle and gardens.