Itinerary in Belgium prior to Rhine River cruise w/Viking

What worked very well for me was 4 nights in Ghent with a day trip to Bruges, and about 6 hours in Antwerp on the way to Amsterdam. You will need to chuange trains in Antwerp anyway (or Brussels). Whichever of the towns you choose to stay in, it will be easy to visit the others. I did not encounter anything I would even remotely call a "tourist trap" in any of these 3 cities. I think you are most likely to find crowds in Bruges and moreso as a daytripper, which could be a reason to base in Bruges to enjoy it in the evenings and mornings-- but I still prefer staying in Ghent.

First question: personally prefer a hotel unless I've hired a car or will be staying a week or more.

Second question: depends on your personal likes/dislikes. To me Antwerp is just another big(ish) city. Bruges (our favourite) is lovely and idyllic albeit somewhat tourist-oriented. Ghent is a bit of a compromise between the two, but it's got a rather "youthful vibe", which IMHO has its positives and negatives.

Bruges or Ghent would work well. One advantage of Bruges is the availability of a day tour to Flanders Field and WWI sights with Quasimodo Tours or another company that offers small group tours. While Bruges can be crowded with tourists during the day (don't forget, we're all tourists), mornings and evenings are delightful. You could also bike along the canal to Damme or visit Oostend on the coast.

Bruges, Ghent and Antwerp are not off the beaten path! In fact, in Bruges you will have nothing but tourists! If you really want fewer tourists and more Belgians, then it is a trade-off because you will be seeing sights that are less worthy of tourism. But let me throw out there Leuven, Mechelen and Lier. All still Flemish architecture, but not tourist cities per se. Leuven is a university town, Mechelen is similar in looks and Lier because it is a mini-Bruges which flies under the radar. If you base in Antwerp these are all really accessible.

For accommodation I like aparthotels. Still self-catering, but the added benefit of a front desk if something goes wrong.

Lavandula

If you have to rely only on public transport it will be hard to find an off-the-beaten-path place that will be appealing. I think your best bet will be the places lavandula mentions: Leuven, Mechelen and Lier. They are not located between the three main cities, but a train journey from there to Bruges will take around 1½ hour. All other places take much lesser time.

You can also stay somewhere in the countryside and use a bike to get to a nearby trainstation. Like the countryside around Damme is very lovely and takes around a half hour to get to the train station in Bruges. If you don’t mind biking, staying in or near nearby Oostkerke is certainly worth to consider too. Sluis just across the border in the Netherlands is lovely but touristy, nearby Sint Anna ter Muiden small but very charming and worth the detour.

Another option is staying in the Zurenborg district in Antwerp with it’s unique turn of the century architecture. Very easy to get to “Antwerpen Centraal” railway station. Lesser fancy, but still nice is the “Miljoenenkwartier” in Ghent. With it’s interbellum architecure a pleasant residential part of the city. “Gent Sint-Pieters” railway station is at walking distance.

You can rent a car for staying in middle of nowhere places or specific places to visit that are hard to reach with public transport. You can think about a DIY tour of the WW1 battle fields around Ypres. Or even go to Middelburg, Veere and Domburg in the Netherlands for instance. Will take a whole day btw. There are many cafees in the countryside, but be careful with drinking.

Just to make sure you know that Amsterdam is good for several days of sightseeing, plus easy access to unreserved, tap-and-go commuter train runouts to places like Utrecht, Leiden, Den Haag, Delft, Amersfoort, and more. Many posters here rate Brussels below the Belgian cities you did name. It is unnecessary to change hotels, if you are willing to go the the train station each morning for a daytrip. Unreserved, low cost trains, if often crowded, especially at rush hours and school hours.

I never use AirBnb because it is so harmful to local housing operations. Have you read that 70% of the housing in Capetown, SA is in use by tourists? Is a tiny washing machine with a four-hour cycle, and a pod coffee machine really worth it?

Normally I prefer to stay in Antwerp, which I may even prefer to Amsterdam, because Antwerp has less of a "spring break" and party-atmosphere. However, I was just in Antwerp, and it seemed like 60% of the underground tram escalators were out of order. That's only a problem with luggage, or if you have any mobility problems, I suppose.

Many posters here consider Bruges and Gent as the two most beautiful medieval town centers [surrounded by forgettable postwar urban sprawl] they've ever seen. But I like the variety of things to do in Antwerp, because it is so much larger. That is, it has tremendous variety, but it's more of a "city" visit.

We leave in two weeks for same cruise (opposite direction, AMA not Viking)! We are finishing in Amsterdam, then taking train to Bruges for 4 nights (our second visit to Bruges, we just loved it, especially mornings and evenings). There is much to see in Amsterdam, as a poster above said, but we have been there several times. I will show the link to where we are staying in Bruges, reasonable and romantic. We will rent a tandem bike, as we did last visit. Use that to get around, and probably cycle to Damme for a fun day. Go to museums, take a couple of tours, etc. Bruges is small, so you can easily get around on foot or using their city bus. We are not big on taking trains to other towns during the day, so I don't have advice on that aspect. On our last night, we will train to Brussels so we can get to the airport for a morning flight to the USA..

Note on trains: the easiest train with the fewest connections, leaves from Schiphol (AMS). So we will get ourselves there when we disembark (Uber). I don't like the ns international website because no matter what date you put in, they populate the field with the day BEFORE you wanted. So be careful, or do as we did, and use the SNCB International app. Also, don't book the train until you are absolutely sure where your ship will be docked - ours will be in Zaandam, not Amsterdam Centraal, like our last river cruise...they do change last minute, which is why we booked train from the airport and not Zaandam or Amsterdam center.

Happy Anniversary, and happy planning!

Our place in Bruges, with kitchen, just outside the main attractions (5 minutes walking):
https://guesthouse-apartment-lady-anna.go-bruges-hotels.com/en/

We love Belgium beer but not fans of huge crowds and tourist traps

Just to be clear... it’s a bit hard to believe you’d be worried about tourist traps in Belgium if you’ve got Amsterdam on your itinerary.

We are okay to do touristy stuff as that's what we are, tourists, but we are not fond of huge crowds which is why we're going on a river cruise as opposed to a larger ship on an ocean cruise. Or hire a private tour guide to take us to touristy spots as opposed to a group tour, etc.