Trip Belgium and Luxembourg

The only thing I want to note is that all public transportation in Luxembourg--bus, train, etc--is free.

That will depend on your interests. For me the must-see were the WW1 sites in Belguim. The VR experience for the Adoration of the Mystic Lamb in Ghent was also very cool. It was also helpful because I'm not an appreciator of art and it gave me the details and history I wouldn't have picked up on my own.

In Brussels build a meal at a good restaurant into your itinerary. For example, a restaurant like Vincent or Le Marmiton, or if budget permits, Comme Chez Soi. Brussels is a 'lifestyle' city with excellent food and this will be a standout in your trip.

Lavandula

You have 7 nights, so 2 maybe 3 locations, from the ideas on here, you will have to pare it down a bunch, with your last night somewhere close to the airport (Brussels, Antwerp, Mechelen)

I will also suggest Ghent, many like Bruges instead, I prefer Ghent, from which you could day trip into Brussels. Antwerp is also nice, probably less so for first time visitors to Belgium, but I enjoy it much more than Brussels, however it does lack the charm of Ghent or Bruges.

For Luxembourg, there must be some interest, either to check it off your list or see something specific. Luxembourg City is the obvious choice, many go for the American Cemetery near there. Bastogne is popular in the South of Belgium for WW2 history, Ypres in the West for WW1 (better with a car for both, or public transport, and pay for a tour of the area)

The Luxembourg City History museum is a good overview. It's also conveniently located to walk along the cliff/walls and past the palace. We didn't go into the Casemets de Bock but they looked interesting.