Hello! I will be traveling solo and by train this May and June for three weeks to both the Netherlands and Belgium and am interested in any insights others might have into my proposed itinerary, especially with respect to nights allocated for certain stops. My interests are wide ranging and I've combed the various posts with respect to Bruges vs. Ghent, etc. Thank you!

Amsterdam--6 nights/5 days (3 for Amsterdam, 1 for Haarlem, 1 for windmill or other day trip)
Leiden--3 nights/3.5 days (Leiden, The Hague, and Delft)
Utrecht--2 nights
[Questions: Should I spend a night or two in Haarlem? Does Leiden make sense as a base for these towns? Does the Leiden/Utrecht order make sense? Am I really missing something if I don't travel to Rotterdam?]
Brussels--3 nights/2.5 days (I know many people dislike it, but the sites are of interest)
Bruges--2 nights (I know it's touristy, but I'd like at least an evening after the buses have left)
Ghent--2 nights
Antwerp--2 nights
Antwerp back to Amsterdam--1 night
[Questions: Is one night sufficient for Bruges to get a feel for the town in the evening? Is Luxembourg worth the long train ride and two night stay?]

Unless you want to move around a lot, I would suggest more nights in Amsterdam with day trips to Utrecht, The Hague and Delft. Except for the eastern extremities of the Netherlands, everything is within an easy train ride of Amsterdam. Last summer, we sent to Utrecht for the day with no problem.

The same goes with Belgium. I think that Ghent is well placed in the middle of the Brussels, Bruges, Antwerp triangle to be used as a base to visit all those towns.

Me and my family actually like Brussels! There are a number of interesting sights in the city, and the art museum is good. We stayed in the St. Catherine area, at Hotel Welcome.

Schedule 1 or two nights in Brugge, depending on the rest of your schedule. For example, if you arrive in the evening of your first night, spend one full day in Brugge, then leave after breakfast of the second night, then you'll be two nights there, but one full day.

No need to move from Brugge to Ghent - they are only about 30 minutes apart by train. Better to stay in fewer places and do day trips that schlep your luggage all over hell and gone - checking in and out of hotels.

We did a road trip starting in Belgium several years ago and one of the highlights was seeing Aachen (just over the border in Germany) which was Charlemagne's capitol and has several sights and relics associated with him. Did this based in Spa - in a charming manor house built for one of Napoleon's generals - this is also a cute town for a brief visit.

Amsterdam can be quite pricey, so if you look for a base, I'd give Utrecht a try.
And yes, you do miss something if you don't visit Rotterdam. Especially since you have more than just 2 or 3 days to play around with.

Gent is a good hub to see Brussels, Antwerpen or Brugge. And Gent, obviously

While most place names do not differ substantially, I'd suggest to memorize the proper language version of the destinations when you rely on train travel in Belgium. While the capital region of Brussels is bi-lingual, train itinararies and information displays are only shown in the respective language in Flanders (Flemish) and Wallonia (French), respectively.

No Cowboy, 1968, don't give him ideas! Nothing to see in Rotterdam. Please let tourists bypass our brave and wonderful city.