ncttc said:
7 to 10 days
Amsterdam is great, but you really need two, maybe three full days there. Rent a bike for an afternoon and explore by bike. Such a fun way to see the city. Go to the windmill brewery located at Brouwerij 't IJ. It's a few blocks east of City Center. The Anne Frank house does not look like a house from the 30s/40s from the outside. I didn't do this when I was there. The Van Gogh museum is really great, however. I loved it. There's a place called beer temple that has Jester King beers in stock, it was wild to see. You'll be in TND in the Spring, so I recommend you head east out of Amsterdam for a day and check out the tulip fields.
If you're trying to fit in Belgium, I'd skip Brussels and go to Bruges instead. Bruges is incredibly charming and really quaint. There's a quote from the film
In Bruges, where Ralph Fiennes describes it as a "Fairytale f***ing town" and he's not wrong at all. I drank Westy 12 at a musty tavern in Bruges. It was surreal.
With your time frame, if you're going to Germany I would guess you'll stick to western Germany? If so, Muenster is a cute little town that I really like. I spent like 5 nights there with a fraulein I met (flex) and loved it. Skip Dusseldorf. It's a stopover town. Cologne has a humongous Gothic church right by the main train station that's awesome to check out. IMO the prettiest towns in Germany are in Bavaria (Munich, Nuremberg and Reutlingen). If it was me, I'd save Germany for its own trip. But I'm biased as I love that country and would move there tomorrow.
As for London, it's a huge metropolitan city. And might be my least favorite big "city" in Europe outside of like, Madrid. It really is awesome though. The Imperial War Museum is amazing. Take a walk on the south bank of the Thames (pronounced "Tims" in case you're like me and didn't know). Tower of London if you're into that era. Big Bend might still be under construction when you're there. There's a big mesh net around it currently. Churchill war bunkers are great. Kensington Gardens and Hyde Park are a nice place to go for a walk or do a picnic. Heaps of fun little pubs.
I can't comment on Paris, unfortunately. But maybe one day. Once you have your cities nailed down come on back and I can give you specific recs (if I've been there)
If it were me, I'd fly into Amsterdam then train to Bruges then to Paris and to London and fly out from there.