I'd keep London in this trip - nice to land in a city where they kind of speak the same language! And it's only about 4 hours by train to Amsterdam or you can take an overnight ferry with trains on each end - I've taken it and at your age it could be rather fun - pubs and such on board - usually lots of younger folk.

Maybe do one short day trip from London to say Oxford - have a brilliant day there trekkingn around the various colleges and museums - dirt-cheap by bus or not much more by train.

Getting on a bike is also a cool idea = Amsterdam has several guided bike tours or you can rent your own for a day and heard to that cow- and sheep-dooted Dutch countryside (come back and ask about that if interested - several here, including some locals can give you good advice on that).

Use large cities as a base from which to take easy day trips by train to nearby regional towns that usually are way different than the large cosmopolitan cities - Amsterdam a great case - day trip to say nearby Haarlem or Leiden or any of many other cool regional towns.

Copenhagen has a surfeit of neat sights a short day trip away- including a Round the Sound jaunt by train going in a circle from Copenhagen to Sweden (en route Lund is a neat university town) and up to Helsingborg, Sweden for ferries to Helsingor (Hamlet's Castle) and back to Copenhagen - travel time ain't much and you see another country.

So spend several days in cities like Copenhagen, Amsterdam, Berlin and do some day trips into a very different Denmark, Holland and Berlin, etc.

Many here IME give great advice if you post more specific questions after this general inquiry.

And strongly look at those Eurail Youthpasses if under 28.

Cheers!

You don't mention Prague but IMO it is a real gem too and a short train ride there from Berlin and scenic one too - as it goes thru Saxon Switzerland with its reddish cliffs along the Elbe River -stop off for a few hours in Dresden (most if not all large stations have luggage lockers) and do Prague -then a short enough train ride to Vienna and from there to Budapest - there is also an overnight train I believe Prague to Budapest.

In Vienna a sweet day trip goes to the nearby Wachau Valley and Melk -famous abbey and then boats on Danube to cute wine towns like Durnstein and then bus/train back to Vienna from there: https://www.google.com/search?q=wach...w=1745&bih=863

Buy all-inclusive ticket Vienna-Melk-abbey-boats-bus-train back to Vienna in Vienna stations.

Saint Petersburg is not to be missed.

<I definitely want to go to Berlin and Amsterdam and London.>

Then I say add Barcelona and call it good. 4 major cities (allowing for travel time in between each) in 18-21 days is perfect.