If you were a kid in your mid 20's and you had a ticket that landed in Amsterdam, you needed to spend two full days in the Hague and then you had 7 days to get to Budapest what route would you take? I am guessing Prague would be on the list but I don't know enough about Germany and kids in their mid-20's to guess beyond that.
Hi James, of all the places we have taken our kids (now ages 21, 18 and 16), one of their favorites was Berlin. We were there for four days and all of us wished we could stay longer, even the 21 year old who usually hates cities (he hated Amsterdam, thought it was cool to see the Colosseum but feels no need to ever go back to Rome, etc). So a route thru Berlin and Prague might be a good choice...
I second the suggestion of Amsterdam-Berlin-Prague-Budapest. Amsterdam-Munich-Vienna-Budapest is another logical possibility. Paris is not a logical detour by train, but OK for flying. He can see an overview of each city (top sights, articles, videos) at http://www.ricksteves.com/europe.
Amsterdam-Berlin = 6 hrs train time or fly Easy Jet, stay Berlin 4 nights
Berlin-Prague = 5 hours train time, stay Prague 3 nights
Prague-Budapest = 7 hours train time by day, or overnight train available
Berlin is a fantastic, young, hip city. If a twenty something gets bored there, they are doing something wrong!