So far, I did not participate on the this threat, because in my opinion Renaissance Brussels Hotel which is located in the 'Quartier Leopold' within a short walk to the European Parliament and other European institutions is a great place to stay for official travel, but not convenient for tourists. If this does not matter, here are some suggestions on public transportation:

To and from the airport by train: BRU is less than twenty minutes from the city centre. From 06:00 till nearly midnight, the Airport City Express links the airport with Brussels South, Central and North four times an hour. Board any Airport City Express train at Brussel Nat Luchthaven (station is located in the basement (level -1) of the terminal building itself), change at Brussel North station and board a train for Brussel-Luxemburg station (from there five minutes walk to the hotel). A one-way ticket costs 2,40 € in second class.

The next underground station is Trone (seven minutes walk on Rue du Trone).