If I had to choose only one building in Cairo that would represent all the different civilizations in Egypt, I would choose the Cairo Opera House. This opera was built in 1869 and reopened in 1988 in the Islamic style in Al Gezeira Island, surrounded by the Nile.
The Cairo Opera House is well known with The Cairo Opera Ballet, the Cairo Philharmonic Orchestra, the National Orchestra of Arab Music, and the Modern Theater Dance group. The Opera hosts cultural salons, art exhibitions and summer music festivals for amateur groups and I used to attend many films during the Cairo film festival every November.
The current opera has 3 theaters: the large 1200 seats, the small 500 seats, and the 600 seats. My favorite Arabic music concert is by Omar Khairat and for Arab singers I would recommend Angham and Ali Al Hagar concerts. Also, you can find a huge opera music library.
You can easily find three options for coffee shops and restaurants inside the opera but my first choice would be Hanager restaurant where you can easily have a seat in the small square enjoying the warm sun in the winter or the air at night in the summer.