What do I do for 3-4 days in Vienna in September?

From Vienna - At A Glance on this website:

▲▲▲ Hofburg Imperial Apartments Lavish main residence of the Habsburgs.

▲▲▲ Hofburg Treasury The Habsburgs' collection of jewels, crowns, and other valuables — the best on the Continent.

▲▲▲ Vienna State Opera Dazzling, world-famous opera house.

▲▲▲ St. Stephen's Cathedral Enormous, historic Gothic cathedral in the center of Vienna.

▲▲▲ Kunsthistorisches Museum World-class exhibit of the Habsburgs' art collection, including works by Raphael, Titian, Caravaggio, Bosch, and Bruegel.

▲▲▲ Schönbrunn Palace Spectacular summer residence of the Habsburgs, rivaling the grandeur of Versailles.

▲▲ Haus der Musik Modern museum with interactive exhibits on Vienna's favorite pastime.

▲▲ World Museum Vienna Four museums in one: Uncrowded collection of armor, musical instruments, ancient Greek statues, and ethnographic treasures in the elegant halls of a Habsburg palace.

▲▲ Albertina Museum Habsburg residence with state apartments, world-class collection of graphic arts and modernist classics, and first-rate special exhibits.

▲▲ Kaisergruft Crypt for the Habsburg royalty.

▲▲ Natural History Museum Big, beautiful catalog of the natural world, featuring the ancient Venus of Willendorf.

▲▲ Belvedere Palace Elegant palace of Prince Eugene of Savoy, with a collection of 19th- and 20th-century Austrian art (including Klimt).

▲ St. Peter's Church Beautiful Baroque church in the old center.

▲ Spanish Riding School Prancing white Lipizzaner stallions.

▲ St. Michael's Church Crypt Final resting place of about 100 wealthy 18th-century Viennese.

▲ Karlskirche Baroque church offering the unique (and temporary) chance to ride an elevator up into the dome.

▲ Academy of Fine Arts Painting Gallery Small but exciting collection by 15th- to 18th-century masters.

▲ The Secession Art Nouveau exterior and Klimt paintings in situ.

▲ Naschmarkt Sprawling, lively outdoor market.

▲ Museum of Military History Huge collection of artifacts tracing the military history of the Habsburg Empire.

▲ Kunst Haus Wien Museum Modern art museum dedicated to zany local artist Hundertwasser.

▲ Imperial Furniture Collection Eclectic collection of Habsburg furniture.

Plus the iconic Ferris wheel at the Prater amusement park.

Visit a heuriger. Attend an opera if the season has started.

The Belvedere is "the" museum to see; and stroll the garden. Tour the opera house and the Spanish Riding School.

▲ Karlskirche Baroque church offering the unique (and temporary) chance to ride an elevator up into the dome.

The elevator in the middle of the church has been dismantled. Its primary purpose was for the renovation works of the frescoes in the cupola, which lasted more than ten years.

You are new here, so one bit of advice: don't use your real name on your profile...along with where you say you live, it is pretty easy to look you up on the internet...

Jojo Rabbit (not my real name, but it is a cool name, no?)

Heard Jojo

What do we like? Architecture (typically churches as they stick around
longer), history, museums (not too many as they really boring really
fast),

Since you like churches, you might like this: https://www.wien.info/en/see-do/sights-from-a-to-z/synagogue-360758

Almost half that list above are museums LOL, but here is one more that I found facinating and not at all boring: https://www.jmw.at/ueber_uns

And JoJo was saying that it is best to keep your name a Myster-e.

Vienna has a lot of interesting Art Nouveau/Secession architecture. Between that and the very many art museums, I happily spent 17 days in the city last year.

My trip report might give you some ideas. My sister and I were just in Vienna and Prague earlier this year.

https://community.ricksteves.com/travel-forum/trip-reports/sisters-in-vienna-and-prague-our-trip-report