Parking in Holland and Belgium

I prefer not to take public transit

Why not? Those countries have quick and frequent trains that will take you almost everywhere.

I'm sure their public transit is great and efficient. Just prefer to drive for this trip.

I thought of renting a small SUV (there will be 4 of us with luggage). Is there a problem driving and parking with this kind of car?

Try to find a car as compact as possible. So try to pack as light or compact as possible too. Most of the time driving around in larger cars is not a problem, but sometimes it certainly will like in parkings and narrow streets in villages.

As Wil noted, parking stalls and curved ramps in paid garages are much smaller than in the US. Many small cities have dug out their town squares for now underground parking. Examples: Leuven, Turnhout. Parking in Antwerp is like parking in Amsterdam-heavily regulated and non-existent. Most suburbs have been redeveloped with modern masonry luxury homes and traffic-calming narrow roads. Business day traffic in the swath between, say, Turnhout and Brugge is very heavy. It's clearly pointless to try to talk you out renting a car. It's not a moral issue, it's a practical one. Hotels charge for parking, if they even have it. Sure, you might find a street space on a given day in, say, Tongeren. What are your plans?

You’re planning to travel to a part of the world where the car isn’t king. Cities, especially the ones with a historical city center are doing everything they can to discourage cars entering the city. Parking is scarce and expensive, streets have 1-way traffic and streets in the very center are completely car-free. On top of that fuel is heavily taxed. That, in combination with the high oil prices, results in fuel prices of over €2 per liter (liter, not gallon!).
On the other hand, public transport is very well organized with a dense network of frequent trains to get you stress and hassle free from city center to city center.

Also, if you’re going to park on the outskirts of a city. How will you get into the city if you don’t want to use public transport?

Like everybody has already mentioned: Parking can be very expensive ! What I do when visiting for instance Amsterdam is park at a P&R site on the outskirts and take public transport from there to the city centre. I did so when I went to Amsterdam last Saturday with 3 friends. It cost me € 1,- for parking and € 7,50 for 4 return tickets by subway to and from the city centre. Cheaper and far more relaxing than driving into a crowded city centre! Parking on the outskirts of town and walk to the city centre might take a long time since a lot of cities have a system of ‘ parking permits ‘ in the area’s surrounding the town centre so you cannot park there and need to walk quite far.

As someone who has done quite a bit of touring around the Netherlands and Belgium by car with a disabled elderly person (who is too proud/ lazy to apply for a disabled parking permit) I would suggest that although it can be pricey it is pretty easy to do. We use google maps and waze to find parking lots close to our destination. Booking.com and airbnb have filters to include free parking.

The most expensive I can recall was in the centre of Utrecht for a few hours - €25.

The cheapest paid parking was the P&R at RAI Amsterdam €1 for all day (as long as you use public transport heading for the centre).