The cross-border ticket is called EURegio (at least in Austria it is) and costs 15 Euros for a round trip; it also includes a day-ticket for Vienna, which normally costs 7.10 Euros. On the OeBB webiste I see that a normal ticket from Vienna to Bratislava (without any local transport) costs 15.80 Euros, so the EURegio ticket is certainly a good deal, even if you don't use it to return to Bratislava.
As Railways noted, the trains run to the new Vienna main station (Hauptbahnhof). Brativlava hl.n. is the main station in town, and Petrzalka is on the outskirts (actually on the other side of the Danube). Bus 93 connects the two. You will arrive from Kosice at hl.n. and can leave for Vienna with a EURegio ticket from either Bratislava station. The main town (very nice, with good restaurants) is between the two.
Last edited by Track; Jul 13, 2013 at 2:04 pm