As mentioned, public transportation in Netherlands & Belgium is great. Before COVID, we often trained to Antwerp just for a lunch break. In northern France, we found we needed a car more often... and then we were punished by the highway tolls. (We don't have those here).
In the Netherlands, you can buy an OV-chipkaart at the airport or train stations...top it up.. and use it to travel by train around the country. We have personalized cards and two "anonymous" cards for visitors staying with us. In our region, they are also good on the buses, trams, and metro. Simply swipe in and out. Trains are primarily Intercity (fewer stops) and Sprinter class. (The Sprinters literally "sprint" from town to town - so LOTS of stops!). Thus, plenty of options for your pace of travel and areas of interest. The NS website and Mobile App can be viewed in English for schedules & costs.
As mentioned, I'd agree not to drive into many of the larger towns - like Brussels, Amsterdam, etc. Traffic patterns and routes can be challenging and parking is so expensive. We went to see a friend visiting in Amsterdam and the garage parking was 32€ for just a few hours - OUCH! (Should have jumped on the train!!!)
My wife celebrated her new Dutch license a few years ago by promptly getting a speeding ticket. She was tagged via a speed camera for going four KM over the speed limit. A couple of weeks later she received a parking ticket (which actually cost twice as much as the speeding ticket). Now, she has the Yellowbrick Parking App so she can simply start it as she gets out of the car. (ParkMobile is also good in BE and NL). These Apps can be set up in English and I have a USA credit card attached to each. As we own a car now, we travel more by car and thus we research the parking Apps available in countries we're visiting. They are SO MUCH easier to use than the various parking machines!
As Wil mentions, there are so many great off-the-beaten-path locales in the Netherlands. A car is perhaps the easiest option, but you can also go by bike! Rental bikes are available everywhere. A cafe down the street from us rents city bikes, racing bikes, and even electric bikes. We've biked to Kindedijk a few times - which is great as there's no charge to simply ride your bike on the path through the windmills.
Last year the law changed and the daytime speed limit on the superhighway dropped to 100 km/hr (It used to be 130 km/hr in many spots). So if driving, do give yourself more time when traveling across the Netherlands. We rue that we now have the lowest national speed limit in Europe. Coupled with the speed cameras, it's been an expensive adjustment for a few of our friends.
Not sure what advice I'd offer on a route. Each of these areas (northern France, Belgium, and the Netherlands) could easily fill your available time individually. I like focusing on just BE and NL, flying into Brussels, and then exploring Bruges, Ghent, and Antwerp (by car or train). Then I'd train from Antwerp to Amsterdam... eventually getting a car if I wanted to explore the countryside. if you want a little exercise, you could rent a bike and take it ON THE TRAIN to those out-of-way locations. Eventually, I'd fly home from Amsterdam.
From the NL, we've been to northern France a few times. Each time, we felt like we barely scratched the surface. When we go to northern France (despite the tolls) we drive - so we can more easily hop from village to village. And we get lost (on purpose) often!
The good news is there are many transport options - so do whatever you're comfortable with and what works for you! For a little variety and a more localized feel, I suggest a little of each: Car, train, bus, tram, metro, boat, or bike. Good Luck!