For the new people in the city, there is a National day in Luxembourg 23th of June, normally there is a nice parade with the army and all the government asociations in Luxembourg, the Duke is there with lots of his friends i mean another Dukes, Kings, Ministers, etc from other countries dressing their original customes from every country. The best point to see it is front of the ArcelorMittal building in avenue de la Liberte, its really nice to see it starting around 10am, but you should arrive early to get a good place. And the night before this event (22nd June) there is a big, big party on the streets of Luxembourg,in all the city center there are many escenarios with live music, bands, DJ's and many activities to see and to do starting around 6pm, also fireworks at 11pm. Normally we walk in groups for all the city centre to see stands, eat and drink with all this music events.
in my opinion its the best night to spend in Luxembourg!