Berlin is the hipster / art / music capital of Europe right now, especially the eastern part of the city. Housing is very, very cheap and it's turned into an extremely vibrant scene. Easy to fly to as well from the US. I'd highly recommend starting there. Make sure you have a plan on where to go beforehand though, there's not one central place to just go and bar hop ... you'll need to make a list of hot spots you want to hit (lonelyplanet.com, etc can help with this) before you land.
I'd go to Krakow next (it works way better train wise to go Berlin > Krakow > Prague > Budapest than any other way). It's the best (and most perfectly preserved) of the old central European medieval cities, and it's a ridiculous party city. Get very, very drunk for very, very cheap in one of the 900 million cellar bars around the city, stumble around the giant squares and hit on stupidly hot Polish girls. You can take a day trip to Auschwitz if you want to see humanity at it's most evil (recommended, though it'll turn your stomach) as well ... then spend that evening in Kazimierz, the old Jewish neighborhood of Krakow which was completely emptied into Auschwitz and is only now returning to full population (though not of Jews, mostly young hip artsy types).
Go on the train from there to Prague, which is fairy tale beautiful and fairy tail partyish. Get offered blow and hookers while standing in front of 13th century churches. Drink gallons of Czech beer, absinth and Becherovka. Hit on so many women so far out of your league you'll have skewed standards for life.
Then on to Budapest, where you can marvel at the ridiculous size of the city ... remembering it was one of the co-capitals of half of Europe for a long period of time. Go to giant markets, eat awesome food and soak in natural hot springs that were built for emperors (seriously one of the coolest things you can do in all of Europe). Walk the chain bridge over the Danube and wander around Buda castle. Hit on more ridiculous women.
Take the hydrofoil up the Danube to Vienna, spend a day marvelling at the stunning architecture and palaces. Wonder why the city is so empty (answer: it's August and the rich Viennese ... aka, all of them ... are on holiday somewhere else). Admire the streets so clean you can eat off of them. Get drunk with me and vadtoy, if we aren't on holiday too.
Fly home from Vienna.
That's how I'd do it.