Netherlands/Brussels/Paris w/ Cologne

It might to be a bit more efficient to go Amsterdam-Cologne-Brussels-Paris.

I always buy advance discount nonrefundable tickets. If you want one stop shopping, go to www.trainline.eu. They do tickets for Deutsche Bahn, Thalys, and TGV at the same prices offered by the rail operators, at least for mainline trains. You get downloadable tickets you can print at home, or if you are not a dinosaur like myself, load them on your smart phone.

Thalys and TGV charge pass holders reservation fees on top of the cost of the pass. Thalys is especially high, almost as much as a deep discount ticket. TGV limits the number of passholders on a given train, so you might not get on the train you want, even if it is only half full.

This is usually a lot cheaper than a rail pass.

Point to point tickets. Buy them as soon as they become available to profit from the considerable discount.
I have some doubts about Cologne. It hasn't a lot of attractions besides the cathedral. Why not an extra day in Brussels, for the city itself or for a day trip to Gent, Antwerp or Brugge, all within easy reach with frequent trains?

For your very first trip to Europe, you need a little more than Internet advice. But if you don't care to go to the library for our host (Rick Steves) travel books, you could look at his many free pages, top left of the screen. In particular, he is a train expert and a railpass expert. It is very likely that railpasses are neither as convenient as you think (i.e. seat reservations required) or the cheapest option. He also has sketch maps with typical transit times. You cannot get all the advice you need from one single thread in one newsboard.

For example, as already noted, Paris is not as well connected to Cologne as it is to Brussels. It is likely that individual tickets bought three months in advance (time is short ... ) will cost the least. But you have to deal with non-changeable, non-cancellable specific rail journeys in all your scheduling then - just like air tickets.

Although I have been to Brussels many times, I don't think it is essential for a first trip to Europe. Even Antwerp is more lively and 'European' (whatever that means.) Antwerp also has a small number of direct trains to Paris, BTW. Cologne is more interesting and varied (and walkable) than Brussels.

This is very much a matter of opinion, but I'd suggest that this will not be your last trip to Europe. On our first trip, around 1985, we spent a week in Paris and a week in London. That was not too much time, counting daytrips like Versailles and Giverney. Note that Cologne has daytrips like Aachen and Dusseldorf available. I'm suggesting that if the scheduling gets too hard, you should consider dropping one of your cities. Our host writes, "assume you'll return."

I like Koeln! Especially Koelsch beer.

Thank you all for your responses. One thing we are looking forward to is good beer. 🍺We do have Rick Steve's latest France book, and picking up others. It sounds like pre-buying point to point tickets is the way to go. This just takes a lot of planning. I had kind of wanted to feel like college kid backpacking thru Europe with no plans but the sensible thing says buy tickets in advance and have a plan. Is it possible to say," this looks like a cool town, let's hop off the train, check it out for lunch, and hop back on a train"?

Is it possible to say," this looks like a cool town, let's hop off the train, check it out for lunch, and hop back on a train"? Not if you use the premium, high speed trains.

Not on trunk line High Speed trains. Yes it is like an airline ticket. The rails have all moved to this model because it is the airlines they are competing with. And "this looks like a cool town.." is a fantasy. These trains zip into big city stations, stop for a few minutes, and then accelerate out to the next big city. If you were vacationing in Germany, there are ways to do this on regional trains with special tickets called Laender, or Qdl, or Happy Weekend tickets where you can hop on and off. But that will have to wait for another trip. Your itinerary is point to point on express trains serving major cities. And the Dutch border to Duesseldorf is the German Rust Belt. No cool towns here.

PS, stop in at Papa Joes Biersalon on the Altermarkt in Cologne. Check out the anamatronic juke box.
https://www.youtube.com/watch?v=JEObQiFWqBM

Sam, I agree with your reply 99.999%. But you overlook Monschau. We met a young German couple who both work at Lufthansa, and neither of them had heard of Monschau. Because it is not that easy to get to from Cologne or the rail line with Brussels, I didn't mention it in my previous reply. And while I am not in a hurry to see it, the Zollverein Coal Mine Complex is, literally, a rust-belt UNESCO World Heritage Site! (The exception that proves the rule.) Luckily, it's easy to see the Bechers' (Dusseldorf KA faculty ... ) photos of the rust belt in other countries' museums and galleries, including the U.S. I also hope to see the suspended-over-the-street subway in Wuppertal sometime, which figures in the film "The Princess and the Warrior."

I'm with Tim on Brussels . Antwerp is livelier in a GOOD way compared to the kind of liveliness you may get in Brussels if you get my drift .

Thank you for the pub suggestion in Cologne. Looks fun!

Also, I actually have looked into Monschau. Agree that it looks like somewhere we would love to see, but I think that will have to be another trip. :-(
Going to look more into Antwerp.

Don't forget Gent, half an hour by train from Brussels. I find it more attractive than Antwerp, and it's only half an hour from Brugge (Bruges), the all-time favourite of foreign visitors.

@ Tim, 2 years ago, I came within a hairs breadth of visiting the Zollverein coal mine museum, but in the end decided to head straight to Berlin from D'dorf airport, and the Wuppertal monorail is still on my bucket list.