This university for music was established in 1875 by, you guessed it, renowned Hungarian composer Franz Liszt. The building is of course primarily a school—but its lively in-house concert series, including chamber music, student ensemble performances and classical works for larger orchestras in several halls and spaces—assures a lot of public interaction with this place’s wonderful classical music tradition. This gorgeous, recently refurbished Art Nouveau building is packed with lovely tapestries and gold-leaf decoration, making it as much a feast for the eyes as it is for the ears.