Music that isn't for tourists:
Volksoper, pick an operetta. Most Viennese thing ever.
If you are there on a Sunday then Vienna Boys Choir singing mass at the Hofkapelle - get there early for standing.
Proper concert at the Musikverein (where the New Years Day concert is held) - might be sold out.
Don't think the Staatsoper does surtitles so not sure what you would get standing. If you have seats then you get individual surtitles on the back of the chair in front.
Food - eat cake at Demel, we love Esterhazy torte. Hotel Sacher and Sachertorte is nice but a massively more touristy affair. Have Kaiserscharrn somewhere. Possibly it will be Spargel season and everwhere will have asparagus on the menu. Pick out different cafes for coffee and have their specialty cake - go to Cafe Hawelka late at night for the buchteln.
Go out to eat at a heurige and drink lots of wine.
Quirky - all the churches that store various body parts of the emperors - hearts in one place, organs in another, bodies in another. V odd, all do tours of the crypts.
Otherwise don't really remember huge queues anywhere. There is more art than you can possibly want to see. Belvedere for the Klimt, Kunsthistorisches museum for well everything and a gorgeous building.
If you don't like horses already don't see the Spanish Riding School. Riders think it's amazing, non riders tend to find it like watching paint dry.