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If you like modern art better, pay a visit to the Danubiana Art Museum on the southern edge of Bratislava. It is about 20km from the city center, so too far to walk. Take bus nr 90 from the National Theater, a taxi, or drive. It is located on the Gabčíkovo Dam, a hydroelectric power plant.
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This is an ancient Roman military camp with archeological findings on display. If you're into all things Roman, you should also consider a visit to the nearby Carnuntum which has a large archeological site and is a few minutes by car from Bratislava.
Permanent archaelogical collections.
Echoing the communist era, the natural science exhibitions have an interesting collection of artifacts and is slowly being transformed into a modern era exhibition.
Most Slovenského národného povstania, called Nový most from 1993 to 2012
A bridge over the Danube river, with its flying saucer-shaped structure housing a restaurant called "UFO". There is an observation deck on its roof, open from 10:00-23:00 daily, offering great views of the old town, as well as the apartment blocks in Petržalka.
Kostol svätej Alžbety
Nicknamed the Blue Church (Modrý kostolík), this is a beautiful Jugendstil church finished in 1913.
For a taste of visual arts, pay a visit to the National Gallery at the embankment between Starý most and Nový most with permanent collections of Slovak and European medieval art pieces, although the temporary exhibitions tend to be far more interesting.