Five weeks isn't enough to devote to more than one or two regions of Europe... I was there six weeks and tried to see too much--as a result I was only in each city for 2-3 days. It worked, and I sure saw a hell of a lot, but just as I was getting to know my way around a place, it was time to hop on the train to the next one.
Anyway, here's where I went:
London, England
York, England
Paris, France
Bayeux, France (Normandy--"D Day" Beaches)
Venice, Italy
Rome, Italy
Florence, Italy
Gimmelwald, Switzerland (somewhat near Interlaken--in the Alps)
Lucerne, Switzerland
Budapest, Hungary
Salzburg, Austria
Munich, Germany
Berlin, Germany
Amsterdam, The Netherlands
As you can see that's a hell of a lot for only six weeks. I'd recommend doing about half that, thought it obviously depends on you and your situation. Personally, I feel the need to go back because I missed out on Spain, Scotland, Ireland, Belgium, Czech Republic, Poland, and Croatia--all places I want to visit.
Anyway, I would HIGHLY recommend London, Paris, and Amsterdam for any trip to Europe. They are each amazing cities in their own right and each offers something different. They're also very close to each other (comparatively) and if your only language is English you'll be fine. I would plan at least five days for Paris and London and at least three for Amsterdam.
Germany is awesome but I noticed (as have others) that it's harder to get by without knowing German. Munich and Berlin are both great cities (they're like polar opposites though). I would recommend Berlin if only for the historical aspect, but it's also rebuilding into one of Europe's premier big cities. If you like techno music at all you will be in heaven because that's all the clubs there play. Munich is very cool too, with its Bavarian flavor. If you go there (Amsterdam also) I would HIGHLY recommend looking up "Mike's Bike Tour". They give you a Schwinn Cruiser and take you out on a guided tour of the city, all in English. I did the tour in Munich and Amsterdam, and both were great! Oh, if you do go to Munich, take side trips to Dachau (site of the first Nazi Concentration Camp), and Fussen (where King Ludwig's famous Neuchwanstein Castle is perched up in the mountains--probably the coolest hike I've ever been on).
OK, my opinion is that seeing the Swiss Alps are a must. I stayed in this tiny little village called Gimmelwald, which is only accessible by cable car from the Lauterbrunnen Valley. I have never seen such gorgeous scenery in all my life. We hiked for three days, and those hikes were just as cool as the Neuchwanstein hike. Switzerland is very distinctive. The people are super nice, the food is to die for (cheese fondue anyone?), and it's so refreshingly "back to nature". The only downsides are cost and season. The weather in Gimmelwald was a clear 60 degrees in AUGUST, so you might want to see what the climate is like in the Spring.
You should see Eastern Europe before it gets completely overrun by capitalism. I had to choose between Budapest and Prague, and ended up going to Budapest because it was covered by my train pass. I was only there for two very rushed days, but what I was able to see was really cool. It's actually made up of two cities (Buda and Pest--go figure), which are separated by the Danube river. Pest is ugly, industrial, and flat, but that's where most everyone lives. The real beauty comes when you cross the bridge into Buda--a gorgeous old-world city, untouched by the ravages of the war (much of Western Europe was leveled by bombs). I have heard a lot of people rave about Prague and Cesky Krumlov--so if you're going to the Czech Republic, pay a visit to those two cities. Get ready for cheap, good beer!
Salzburg Austria was one of my favorites. So German and yet so not. It's a beautiful city, with a huge fortress perched on a hill at its center. It's widely known as the setting for "The Sound of Music" so there's tons of SoM memorabilia there (as well as a bus tour of the exteriors used in the movie, which was entertaining). It's main claim to fame is that it's Mozart's birthplace--you can tour his old house. Unlike Germany, the people of Austria are willing to speak English (for the most part) so it was easy to communicate.
I leave Italy for last. It's such a huge and important place that it will eat up more than half your trip if you let it. I visited three cities (four if you include a day trip to Pisa to see the leaning tower), and really enjoyed myself. I went during the peak tourist season (mid-August) so it was really crowded (and HOT!) while I was there. I'd say go to Rome first--there's too much history there to bypass it. Florence is next (really cool place, birthplace of the renaissance). Venice is really cool also, but is fairly limited when it comes to things to do (my favorite activity was just sitting in some old back street imagining what life there must have been like in the 1500s). Venice is also pretty expensive. But it's also romantic... nothing beats a candlelit italian meal at some little place by the grande canal. And don't believe the rumors about the smell of the canals--they just smell like seawater for the most part. I wouldn't advise swimming in them, however!
Well anyway, that's enough for now. If you have any other questions, I'd be happy to do my best to answer them for you. Europe is such an amazing place. I can't wait to go back. Probably the most important piece of advice I can give you is to keep an open mind while you're there. Lots of things are done differently (but not inherently any worse or better than here) so try to respect the European way of life and blend in. Be adventurous and don't default to McDonalds just because there is one on every block (alhough I must admit that I went to Burger King a couple of times

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But in the end, have fun--I'm jealous!
l2c
P.S. DEFINITELY invest in a guidebook. I like the Lonely Planet series, but lots of people buy the "Let's Go" and "Rough Guides" series also.
P.P.S. It basically goes without saying, but don't bring suitcases. Bring a nice big backpack and live out of that. Pack light and you will thank yourself later.
P.P.S. Lastly, check out
this web site. It's got tons of helpful info (including some pretty good forums).