Best way to see Holland and Belgium highlights and tulips in 8 days

Trains will easily take you between these places. A car can be a detriment rather than a benefit when you're dealing primarily with city visits.

April 2019 we took a river cruise from Amsterdam that went to your locations and tulips fields etc. Ck it out it is Gate One travel and tour name is tulip cruise. I highly recommend we went and loved it.
About 100 passengers. Really nice for a reasonable price..

It is doable, although rushed (which you're undoubtedly well aware of):
1. Fly in and out of Amsterdam (Schiphol airport)
Take train from Schiphol to Gent (2 to 3 hrs, depending on type of train) or Brugge (half an hour longer)
2/3. Stay there 2 nights, leave late afternoon 2nd day, giving you a full day for Brugge and the better part of a day for Gent
Take train to the Netherlands. Stay in Amsterdam (expensive and crowded) or Leiden (historical city, more relaxed and cheaper, direct express bus to the Keukenhof, 20 mins by train from Schiphol airport)
4. Have half day for the Keukenhof, rest for exploring Leiden
5. Day trip to Amsterdam (40 mins by train)
6. Leave for Schiphol for return flight.

Maybe one or two days to fill in, depending on your 8 days being in- or exclusive of flight days:
Extra day in Belgium for day trip to Brussels (30 mins from Gent) or Antwerpen (1 hr)
From Leiden day trip to The Hague (Den Haag; 15 mins away) for the Mauritshuis (Vermeer, Rembrandt) or the Escher museums; can be combined with Delft (10 mins from The Hague); or day trip to Haarlem (20 mins) with the Frans Hals and Teylers museums; or an extra day for Amsterdam. The train from Leiden to Haarlem goes right through the tulip fields!

In Holland, why don’t you visit The Hague and Leiden?

in Belgium, Why don’t you consider Antwerp, the Diamond City and also the famous Flemish painter, Rubens and Gutenberg city who invented .printing.
In the French speaking region not very far from Antwerp is Liege, Huy and the water damp of Gillette and Eupen. Stavelot Abbey and Spa in the same area are very interesting and beautiful to see.
Very nice a little further but quiet area and more bucolic area is the countryside in the Hainaut boot near Chimay, (beautiful castle) Beaumont, Lobbes and its wonderful millennial church ( might need to rent a car for this part). Bastogne is also very interesting for Americans interested in the 2nd world war with the Ardennes Battle.

I do not like Amsterdam. Bruges is much more beautiful and friendlier.
Tulips fields are a beauty.
In Holland, I like The Hague, Leiden and Gouda and its wonderful market.
Holland islands ( Zeeland) are also wonderful.
Also in Holland, unless you are prepared to open your purse, food is really not nice, especially in Amsterdam.

Check also flights to or from Brussels.
Do not miss Brussels Grand Place

However you organize things I’d try to do Keukenhof on a weekday. I’d also get there at opening.

I was on the RS tour last April and our visit happened to fall on a Saturday when they were having a Flower Parade (April 13, I think). We got there right before it opened so not bad but it was a madhouse when we left.

Gutenberg city who invented printing
Gutenberg had its business in Mainz (Germany), but Antwerpen indeed has the Museum Plantin-Moretus, preserving the printing offices of one of the most important publishers of those days.

Thank you for these good ideas to consider in my plans!