
Semper Opera House (Dresden)
The opulent Semperoper (Semper Opera House) was completed in 1841. It has had its share of problems though, burning down in the 1870s and reopening in 1878, bombed in World War II and reopened in 1985, then damaged in the huge floods of 2002. However, the premieres of The Flying Dutchman, Tannhäuser and Der Rosenkavalier were held here, and the repairs and restoration have returned the building to its former glory.
Deutsche Oper am Rhein (Düsseldorf)

The city's opera house.
The Philharmonie in Cologne

For classical music, Kölner Philharmonie is the place.
