Parking throughout Benelux and western Germany

The best strategy is to look for parking garages (they are present in many cities), and park there, instead of dealing with street parking. Some hotels do have parking, others don't. Those which have parking almost always charge for it in big cities.

This being said, driving in this area is fairly easy. You just need to be patient within cities.

Bigger hotels commonly have either on-site parking or an affiliated garage close by, but it's almost never free of charge. The price varies widely between cities and within the same city, depending on the area.

Brussels and Amstedam are two of the worst cities for driving in Europe. Parking is vary scarce and expensive. Unless you absolutely have to, I would not use a car here.

With the exception of the Munich, parking is usually cheaper and more widely available in German cities.

Just remember in Germany if you park in a parking garage to pay at the kiosk before trying to leave the garage. Or you might have some angry Germans behind you honking...:)

Will you pick up the car upon leaving Brussels? If so, then that's one bigger city off the list. If you stay in a smaller town like Haarlem, you can daytrip into Amsterdam by train (20 minutes each way). Or if driving to Amsterdam, Rick suggests following signs from the freeway to the suburban P & R (Park & Ride lots) where parking cost 8 euros/day, up to 4 days, much cheaper than the downtown garages, and includes transfer into the city.

"I'm excited at the idea of driving, as we like visiting places off the beaten path"

I think needing a car to visit places off the beaten path is a myth. I'm often criticized on this site for eschewing large cities (82½% of the places in which I have stayed are under 50,000 pop), but I have never needed to rent a car.