Centraleurope and I are playing tag team I guess. Also check the operett theater. Its a few blocks from the Opera house, very grand and it often has performance with English subtitles. In both cases splurge for the best tickets available, men at least put on a sports coat and tie. Intermission at the Opera is fantastic with the bar and the balcony looking over Andrassy ut and intermission at the Operett if you spring for the good seats they take you to a private parlor where you share a table with a few others, talk and enjoy wine and hors d'oeuvre. Since as Centraleurope suggested, the music is an important part of the culture in Budapest unlike some nearby cities the performances are for Locals and not staged for the tourists. You will be surrounded by Hungarians (especially in the better seats) and have a chance to meet and interact with the people. I have traveled more than average and I have never met a better people.

Overnight trains are not good for any light sleeper - even in private compartments there is noise all night - train track noise, train whistles, station speakers, etc. so no lighgt sleepers should eschew the train or arrive wiped out and ready for bed!