Note that, if you get the train from Vienna to Bratislava, you have two options: a spangly new double-decker train to Bratislava-Petrzalka, or a clattering old railcar to Bratislava-Hlavni.
I would always opt for the latter. Bratislava Hl St (main station) is close to the centre of town, with a good tram service towards the old town. Petrzalka is miles away. There is a bus service from there, though, but the taxis have outrageous fares.