Here's a whole bunch of information that would maybe be helpful if you are planning on doing a trip like ours, or even just to one of the cities.
Best purchases for the trip:
Shoes. I was really happy to have bought a pair of sneaker-style Rothy's. Yes, expensive, but we walked a lot and the really held up comfortably. Easy to travel in as well.
Clothespins. We packed very light, so had to do some laundry along the way, and only had a dryer in one place. These made it easier to hang up underwear, socks, etc.
Laptop. While it was a pain to lug around, it was really nice to be able to easily stream some TV during downtime, and it was way more convenient to buy tickets, etc on the computer than on our phones.
A good international plan. We didn't have a ton of data available to each of us, but we had enough that we could turn on google maps, look up where we were going, and then turn off data roming again. It was really helpful getting around, as the city maps we bought often weren't detailed enough to be of much use.
Luggage. I think that Pete's suitcase was probably the best of the four. Jax and I took our backpacking backpacks, which I didn't mind but he hated. The combination of backpack+roller bag+built in carry-on was really great, although it was definitely snug.
Things we didn't need:
Travel pillow. Yes, it made the plane ride marginally more comfortable, but then we had to lug them around the rest of the time. Not worth it.
Places we stayed:
We used Airbnb in every city, and generally had good experiences. The one thing that really got me was the total lack of fire safety in the apartment buildings. We were never on the first floor and there was never a fire escape. I am not normally paranoid about this kind of thing, but it's just something to be aware of.
Getting around:
Pete booked all of our train trips, so I know very little about the logistics of that. However, I do know that if you book in advance there are some really amazing deals (I think we got from Amsterdam to Paris for something like $30 each). With one small, flukey exception, train travel was incredibly easy. (Definitely be on time for your train. If it says it's leaving at 8.32, it's pulling out of the station at 8.32).
We also exclusively took public transportation (three exceptions: our tour to Terezin started in Prague, our windmill tour started in Amsterdam, and we took a taxi to the airport in Paris). Berlin's system was the most comprehensive and cost effective, but they were really all good. In every system trains/trams/busses ran frequently and took us very close to where we wanted to go. Amsterdam's was the least efficient, and Paris' had the most detours and the most warnings about pickpockets, but there was really no reason to get a car or use a taxi in any of the cities we went to.
But we don't speak German/Czech/Dutch/French:
Yeah, neither do we. Pete learned a little German before we went, and we all learned how to say please and thank you in each of those languages. However, in the tourist areas, everyone speaks English. Even the menus were in English. In some cases having greater fluency with German or French would have been helpful, but it really wasn't a problem.
Tips for the best things we did:
Vienna:
Get the ViennaPass. It really covers just about everything that you want to do, and definitely saves money.
If you want to eat at Figlmueller, make a reservation. We bypassed a line that was at least an hour long.
In Vienna our favorites were the Schonnbronn Palace/Grounds/Zoo, climbing the tower at St. Stephen's Cathedral, and Prater Park.
Prague:
We had a really good dinner at U Medviku, a traditional Czech place in Prague 1. It's a little distance from the main tourist area, but definitely walkable and worth it.
If you want some Holocaust history without the emotional devastation of visiting Auschwicz, I recommend seeing Terezin. We booked our tour through TripAdvisor, and thought that the 6 hour was just the right length.
We had heard that Prague was going to be cheap, but I think that's a holdover from travel in the early 2000's. We didn't find it more or less expensive than any of the other cities. They don't use the Euro, however, so it does make converting the cost in your head a little trickier.
In Prague our favorites were the Prague Castle complex (it's worth climbing the tower) and the synagogues in the Jewish Quarter.
Berlin:
Visiting the Reichstag Dome is free, but requires a reservation, which can be done online. I highly recommend both making the reservation in advance and going here.
The public transportation system in Berlin is extremely comprehensive, easy to use and safe; there is really no reason to get around any other way.
In Berlin our favorites were the the East Side Gallery, the Spy Museum, paddle boating in Treptower Park, and lunch at KaDeWe.
Amsterdam:
Tickets for the Anne Frank house become available two months before the visit date, and the timeslots go quickly, so if you want to go, definitely book online in advance. That said, it's still very crowded, so be prepared.
There are a thousand possible canal cruises. We did this one because it was open air and a smaller boat, and I would recommend it.
Definitely eat at Pancakes Amsterdam.
I cannot say enough good things about That Dam Guide's windmill tour. It was my favorite day of the whole trip. Just a wonderful wonderful adventure, and absolutely worth the money.
If you want to try traditional Dutch food, we had a delicious dinner at The Pantry; reservations are required.
The "escape room" at the Rijksmuseum was a really cool way to see the museum, and definitely kept the kids entertained. We saw lots of families doing it, but plenty of adult couples doing it as well. There's a limited number of spaces each day, so definitely book in advance.
Our favorites in Amsterdam were the Windmill Tour and the escape room.
Paris:
There are so many great places to eat and the city is so huge that it doesn't make a ton of sense to travel from one part of the city to another just to eat somewhere. However, if you're already in one of these areas, we had excellent food experiences at
Cocorico, very close to the Musee d'Orsay/Tuileries Garden. Get the roasted chicken.
Ice cream, in Montmartre
Chinese noodles, near Hotel De Ville
If you're near the Catacombs, stop by Moisan LeClerc for bread, specifically the brioche. It's a small bakery and they don't even have a website, but it was the most amazing pastry we had the whole time we were in Paris.
I cannot say this enough: get tickets in advance for everything in Paris. We walked past so many lines and did not pay a cent more to get into Saint Chapelle, the Louvre, the Musee d' Orsay and the Catacombs.
If you want to see Versailles, absolutely, unequivocally, book a tour. We were really happy with our choice to get a tour of the palace itself but we were free to explore the gardens on our own. We did this one, but I'm sure there are others. It was a little more expensive than just going on our own, but skipping the line alone made it worth it. We didn't find it difficult to get to Versailles on our own, and it saved us a lot of money and gave us good flexibility (just triple check to make sure all of the train lines are up and running). We found it worth the money and the wait in line to rent a golf cart to tour the grounds.
Do a food tour. We'd heard really good things about Paris By Mouth, but they weren't running the days we were in town. We did this one through With Locals and had a really great experience with Zoltan. The price included tons of food for each of us.
Our favorites in Paris were the Louvre (a real surprise to all of us), the Catacombs, the grounds at Versailles and, of course, eating.
I think that's it. It's a little weird to be home and have this epic thing that I'd been planning for so long be behind us. It was a wonderful experience.