You have to go to Berlin... no matter what the cost.
It was the best place out of Europe when I went (mind you I was 14 at the time, nearly 15 haaha). I went on a free walking tour of Berlin, which was bloody fantastic. They ask for donations at the end of it, but even giving the tour guide (I got some Aussie chick from Adelaide, it was awesome) 20 Euros would be awesome. I then went on a paid tour, which was alright, but it was still pretty freaking awesome. They basically take you through all of the touristy areas of Berlin such as the Brandenburg gate, Unter den Linden, then the Holocaust memorial, general cool shit like that. You could spend a few days easily there if you're going for just a week.
Another suggestion I would make (from my limited experience) would be Italy. Rome and Florence are alright cities, dont get me wrong. But when I went, I found going to museums consecutively for about a week did get rather annoying. Definitely see the Colosseum. Personally, I'd skip Venice. My family and I spend a night there and left the next day. I guess you wouldn't call it very family-ish, but rather for romantics and shit like that. Plus when I went, I got maccas for dinner, and it ended up costing 15 euros, which equated (at the time) to $30 AU. This was for 2 meals. At that price, I could have bought at least 4 meals back at home. I also ended up spilling both my brothers and my drinkings when tripping up the stairs at said mcdonalds (although it might have been Prague, cant remember).
Speaking of which, Prague was an absolutely awesome place to go. Architecture and shit like that is just stunning. I went to that museum type place or something and found it to be quite interesting. Although I dont know if you would include it in a week-long holiday to Europe though.
I'd also mention Poland was freaking amazing. Warsaw was alright - the only thing I did there was see my uncle but if you're passing by, definitely go to Krakow and go to Auschwitz. It was ..... a unique experience walking through the camp in the afternoon snow. Although I'm not sure if you'd go there in a 1-week holiday.
Paris, I thought was actually quite dirty, but it may have just been the hotel where we were staying. If you find a nice place, definitely go. The Louvre is massive, and you can easily find yourself lost in the depths of all the stuff they have there. Plus the Eiffel Tower is there, I mean, come on.
Budapest was awesome. Although I think it might be a bit out of the way for a week-long trip. The House of Terror was absolutely brilliant.
Vienna was awesome, although I cant really remember specifics. The only real experience from there was some punk/skinhead dude with a radical purple mo-hawk wearing black clothes coming up to me and speaking this insanely fast German at me. I only really knew a few words of German, so all I could say was 'nein' when he was finished speaking ahahahah.
As for the rest, I cant really say.
noice