London, paris and amsterdam are all " must visit " places in europe. Aachen isnt. And its a detour from paris to amsterdam. Instead stop in either brussels of antwerp. Have a good belgian beer and a waffle with cream. And steamed mussels.. Mmm mussels. (The shellfish kind... The other kind u can experience in amsterdams red light district, but we'll get to that later...)
From antwerp to amsterdam I'd suggest driving along the Delta Works (wich are huge stormsurge-walls that protect a third of the netherlands against flooding).. Or if your into windmills visit "kinderdijk" wich has one of the best preserved dutch irrigation mill systems of all).
In amsterdam I would skip Madamme Tusseauds.. Its a ripoff. Also skip the amsterdam Dungeon.. Also a ripoff.
If your into curture the the Rijksmuseum is a must see.
But offcourse as american you want to have a bit of the green... Enjoy it, but as mentioned earlier, have a pal looking after you. never buy anything narcotics wise on the streets. (There's been word that some are selling heroin as coke.. Also lookout for other pills etc.)
And finally... Yes.. Offcourse you need to visit the red light district. Use all the "facilities" if you desire.. But be safe while doing so :-)
(Ps: dont go arround " omg'ing" everything u see... Most europeans like, but frown at americans. We tend to find them too loud and arrogant. Be respectfull in europe and you will be treated as a welcome guest!