I haven't been to Utrecht or Dusseldorf, so I can only comment on the first part of your itinerary.
When I went to Belgium, I flew into Brussels and took the train to Brussel-Centraal, checked my luggage in a locker there, and did a little walking tour before heading to Ghent, where I spent the first three nights. I liked it enough to go back for a half day a few days later so I could visit several of the museums. The Royal Museums of Fine Arts are absolutely worth a visit if you are museum lovers, as you say you are. I also really enjoyed the Musical Instruments Museum.
I also did a day trip from Ghent to Bruges. I felt a day trip was sufficient to get a feel for Bruges. I rented a bike and rode along the canal to Damme, where I had lunch. That was actually my favorite part of the day. Bruges is very pretty but didn't feel especially authentic to me.
Museums in Ghent I especially liked were the Museum voor Schone Kunsten and the Huis van Alijn.
I agree with kblur that 4 nights in Antwerp is more than necessary, but there is absolutely no need to add nights in Brussels or Bruges, because it is easy to see them as day trips from Ghent, and there's no good reason I can think of to relocate so often. I would subtract time from Antwerp and add it elsewhere.
I only got to spend one afternoon in Rotterdam, but I loved it and wished I had more time. Yes, it's a modern city, completely rebuilt after WWII, but the architecture is absolutely fascinating. Everywhere else you're going, you will see lots of gabled roofs and will be saturated with charm. But Rotterdam is different and worthwhile, in my opinion. I especially enjoyed the Museum Boijmans Van Beuningen.
That said, Delft is just so relaxing and lovely, and if you like Vermeer, it's worth spending some time there. Not much of his art is there, but seeing his hometown and just strolling along the canals is a delight.
And don't miss the Mauritshuis in The Hague, where you'll see several Vermeers.
I wonder why no one so far has asked why only two nights in Amsterdam. Of all the places you're going to, it's the city with the most museums, including the Rijksmuseum and the Van Gogh Museum, among the best in Europe. Plus from there you can do day trips to Leiden, Haarlem (the Franz Hals museum there is also fantastic), and the many charming towns and villages to the north (Edam, Hoorn, Zaanse Schans, and Enkhuizen, to name just a few).
While I didn't ever make it there, everyone who has says the Kröller-Müller Museum is very much worth a side trip.
Lots to think about. Whatever you do, I'm sure you'll have a great trip.