You can check trains timetables and prices from one city to the other at the 3 official national railways websites (providing English pages here): ÖBB, CD and ŽSR.
Vienna is a splendid city. I won't really add much to the abundant literature about Viennese culture, festival, music, and museums, but simply describe how much I enjoyed Viennese cafes.
They are really an institution, and as soon as you enter you feel the contrast with the busy and cold (if like me you visit in winter) streets outside. Always very quiet, very often smoky, cafes are the place where locals would spend hours reading the omnipresent newspapers or a book; often having just one or two coffees.
Everybody should feel at ease and not pressured to consume more or leave for another place. Like Irish pubs every cafe has a story, different decorations or themes, and often a good few legends of the famous character who used to go there. You really haven't been in Vienna if you haven't spent some time in one of those magic places.
Brno, in Czech Republic, is a quite attractive and interesting city, despite not being a main tourist destination (apart during the moto GP that takes place here).
Actually that is probably one of Brno's biggest advantages: contrary to Prague most of what you see here, including bars and restaurants, is for the local residents and not for tourists.
The city center is full of historical buildings and churches, and from both the Spilberk Castle or Petrov Cathedral you can enjoy a great view of the city.
Bratislava, our third train stop, is a charming little (450K inhabitants) city, and of course the capital of Slovakia. What really impressed me about the city is the old part of the town center.
Quite forgotten years ago, people are now rediscovering the beauty and quality of life of the old town, and as a consequence the whole area is under renovation at the moment.
At every corner you see the contrast between the old, ruined houses and the freshly renovated ones.
The contrast is even more enhanced by the bright colors used for the new coats of paint.
Considering how close these three cities are, and how cheap is to move between them by train, it would really be a pity to spend some amount of time in just one of them without visiting the others. Happy train ride!
