When we were in Bad Pyrmont, Germany we stayed at Hotel Schaumberg. It was a great location for us, the room was great for the three of us, and the food for breakfast was awesome. I would stay there again.
When we were in Belgium we stayed with our Belgium family in Ottingies (south of Brussels). It was great. We'd stay there again also :-)
Our Airbnb in Normandy was excellent (photos). We would highly recommend staying there. The host was amazing. The area around our Airbnb -- known as Les Bateaux -- was a short walk down to the beach and a great location to explore D-Day historical sites, memorials, and museums.
In Paris we stayed at the Hôtel de Roubaix (6 Rue Greneta, 75003 Paris, France). I thought the place was average and good for our situation. It was easy to get to and easy to navigate to the Louvre for sure by walking. Also it was easy to get from the hotel to the airport via a big transit hub that was just down the street (10 minute walk). We used Booking.com to reserve our rooms.
Our Airbnb in Rome was great (photos) the location was about a 30 minute walk to the Vatican and then a 30 minute walk to the Colosseum. The host was excellent and very helpful in helping us get to and from the airport. The place included a full kitchen, air conditioning, and was roomy enough to spread out. I'd recommend staying at this location if you travel to Rome.
The next stop was Amsterdam. I spent a lot of time trying to find a good AirBNB but wasn't successful. I also looked into some of the nicer hotels but the prices were 3x what we ended up paying. We ended up at Hotel Isis (Spreeuwenpark 17, Amsterdam Noord, Amsterdam, 1021 GS, Netherlands) via Booking.com. It was definitely spartan but clean. And I felt safe in that part of town. The walk to the ferry and taking the ferry was fun and different. Having the ferry stop in Amsterdam at the Central Train station was a bonus. I probably wouldn't stay there again but if you are in a pinch it is doable.
After Amsterdam we made our way for a 1-night stay in Berlin at the Hotel-Pension Cortina (Kantstr. 140, Charlottenburg-Wilmersdorf, Berlin, 10623, Germany). This hotel was also booked via Booking.com. I was also not able to figure out a good AirBNB option in Berlin, and since we were staying just one night I wasn't as detailed in my research on this hotel. It turned out fine, but just like Hotel Isis it was spartan but clean. Our room was on the shared courtyard so it was noisy at night. I definitely would have considered some other hotels if I wanted more comforts.
Our last night of the trip was spent at the Marriott Sheraton at Frankfurt Airport. It was by far the best hotel room we stayed in during the trip, and given that we just walked up and got the room, the price was pretty affordable. It was a great ending for the trip. Solid night sleep and great shower in the morning. The walk back to the airport was easy, and we got through security/customs/immigration without any issues.