Well, that's just silly.

Many trains a day between BUD and BTS, though the reliability may be suspect (same will apply to VIE).

Scored a VERY cheap Biz fare a couple of years ago to BUD, took the bus to the main train station and purchased a direct train to BTS. Sadly the train was a few hours late, but it got me to Bratislava.

It's a lovely city, though most Western tourists won't want to spend more than a day or two there, but you can take a direct train to Poprad to go explore Vysoke Tatry.

If you are somewhat adventurous, you can bus/train it to Poland (RomeToRio.com has some very good suggestions).

Going to Kosice (hopefully next year) and to Vysoke Tatry next year for first time in 30 years (OK, never been to Kosice) with a one day layover in Vienna. That is another wonderful city to visit, and one that has boat connection to Bratislava, if that's what floats your boat