Hi, you should do all :-D And some more...
Being Czech, I would recommend Prague. Unfortunately we still do not have post about Prague, but it will come... Be careful of taxi drivers, and try some local beer. Czech is really famous for cheap beer, great night life and good food.
Berlin is also nice, especially the contrast between west and east part (behind the wall) :-)
Vienna, well it is relaxed and nice city.
Also in the proximity you have Budapest, which we will post about in near future and Bratislava

All these cities has great deal to offer because they played major role in Europe history over the centuries.
I would say that 2 days stay in each of them is long enough to walk around and enjoy the local life little bit. English language is not a problem, you will find lokal people speaking English everywhere.
What is best that there is really good connection between all these cities by trains & buses. I prefer trains. Ceske Drahy operate trips between these towns for really reasonable prices.
You can also check Student Agency / Regiojet for some offers on bus / train tickets. It is well known Czech bus & train operator.
Enjoy and do not hesitate to ask more questions & let us know how your trip was...