So, we weren't the only ones wondering what Guillaume actually does in Brussels and what this "working visit" is all about, the people over at Wort had the same questions and did some research. Two articles about the matter can be found over at Wort and Voix (the French version of Wort).
The first two weeks of what, in my humble opinion, would better be called internship, the Hereditary Grand Duke will spend with Viviane Reding, the Luxembourgish Vice-President of the European Commission who is the Commissioner for Justice, Fundamental Rights and Citizenship, and her staff. Together with them, Guillaume will take part in all the meetings and sessions that will occur during this two weeks. He will also visit the different Directorate-Generals that he will encounter while working for Madame Reding.
During his time in Brussels, everyone's favourite Hereditary Grand Duke will also meet with two other members of the European Commission, the Commissioner from Denmark Connie Hedegaard, who is responsible for Climate Action, and from Latvia Andris Piebalgs, who is in charge of Development Aid matters.
The third week, Guillaume will pass time with the permanent representation of the Grand Duchy to the Europeen Union. During this time he will take part in meetings of the COREPER (Commitee of Permanent Representatives), the commitee prepares the work of the council of the European Union.
The German version of Wort isn't shy to point out that our dear Guillaume must feel like Brussels is a second home for him as he got family in the royal palace there (Grand Duchess Joséphine-Charlotte was a born Princess of Belgium and sister of the current and former Kings of the Belgians), one should also not forget that he has other family members living in the Belgian capital like his aunt Archduchess Marie-Astrid and as Wort kindly mentions, there is always Stéphanie... Though it made me smile a little, how they mentioned her with a lot of maybes, perhapses, possiblys and a never-ending subjunctive, after all she is only the alleged girlfriend of the heir to the Luxembourgish throne.
Sources: Europeen Commission - Viviane Reding, Connie Hedegaard, Andris Piebalgs, COREPER; Wort