You can easily hang out a few days in Berlin, you're a fool if you are only going to stay there just for a day at the match 
Personally I don't understand people who want to see Europe in a week, so I'll limit you to a much smaller regional trip: stay within the German(ic) phere of influence.
Prague is not too far from Berlin and a very pretty and nice city. Spend a few days there as well.
That leaves a few days somewhere else.
Depending on your interests you might have a peek at (listed counter-clock wise from Berlin)
- Cologne (Köln). A very nice German city in the west. The closest you're going to get for a feel of Holland (save going to Holland itself)
- Bavaria (Munich). The south of Germany is very different then both Cologne or Berlin. Not my cup of tea, but a place to visit nevertheless.
- Vienna. Heart of the Austrian Empire. A bit too baroque for me.
- Budapest. Second heart of the Austrian Empire. Much better then Vienna.
- the Croatian coast. Beautifull, sea and sun. Perhaps a bit too far from Berlin. Drinks and party.
- A trip to the region of The Tatra mountains (Slovak-Czech-Polish border region). Beautifull nature in those places that have not been pillaged by communist exploits of coal-mining)
- Poland (Krakow comes to mind, Warsaw hasn't got the same appeal.) An unpleasent trip to Auswitz (nearby Krakow)) could bring you to terms with European heritage. Not much fun, but impressive nevertheless.
It might save you from cheering for the Germans winning the worldcup, so well worth the effort
Berlin-Prague-(Tatra-)Berlin

Personally I don't understand people who want to see Europe in a week, so I'll limit you to a much smaller regional trip: stay within the German(ic) phere of influence.
Prague is not too far from Berlin and a very pretty and nice city. Spend a few days there as well.
That leaves a few days somewhere else.
Depending on your interests you might have a peek at (listed counter-clock wise from Berlin)
- Cologne (Köln). A very nice German city in the west. The closest you're going to get for a feel of Holland (save going to Holland itself)
- Bavaria (Munich). The south of Germany is very different then both Cologne or Berlin. Not my cup of tea, but a place to visit nevertheless.
- Vienna. Heart of the Austrian Empire. A bit too baroque for me.
- Budapest. Second heart of the Austrian Empire. Much better then Vienna.
- the Croatian coast. Beautifull, sea and sun. Perhaps a bit too far from Berlin. Drinks and party.
- A trip to the region of The Tatra mountains (Slovak-Czech-Polish border region). Beautifull nature in those places that have not been pillaged by communist exploits of coal-mining)
- Poland (Krakow comes to mind, Warsaw hasn't got the same appeal.) An unpleasent trip to Auswitz (nearby Krakow)) could bring you to terms with European heritage. Not much fun, but impressive nevertheless.
It might save you from cheering for the Germans winning the worldcup, so well worth the effort

Berlin-Prague-(Tatra-)Berlin
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