Here is what I have recommended before to people who were going to be in Vienna for Saturday night and Sunday till late afternoon. I'm not sure if you have a night there as well, so this may need to be further cut down.
This is malleable based on your interests, but here is what I would do:
-If you get in early enough on Saturday, I'd go see an opera or ballet at the Wiener Staatsoper if something is playing that night. If nothing is, look into other venues for classical music; Rick lists many of these in his guidebook. Last time I was in Vienna, I went to a concert here and enjoyed it (musicians were pretty good, and the church is GORGEOUS): https://classicexclusive.com/en/home/
-Walk by St. Stephen's Cathedral at night; I think it's the most beautiful building when it's lit up at night. A significant portion of Rick's St. Stephen's tour focuses on the exterior architecture, so that would be worth reading. The inside is beautiful too, of course, so it would also be worth popping in during opening hours to see that as well. I believe they do concerts in there, so maybe you could combine the two for your Saturday evening entertainment (I can't speak to the concert quality, having not attended one there).
-Start the day following one of Rick's Vienna walks to get a sense of the city center (District 1); if you haven't had a chance to get inside St. Stephen's, you could do that now as well, though pay attention to the Mass schedule as you'll be there on a Sunday. When Mass is in progress, you are only allowed to enter the Nave if you are attending Mass (though you get to do so for free then); when Mass is not in progress, you can enter the Nave for a fee. And you can always stand at the back and peer through the gate without paying anything.
-See the Lipizzaners perform at the Spanish Riding School at 11 AM (I think this is specific to Sundays...not sure what the scheduling/options are on other days of the week)
-Go to a cafe for a lunch and leisurely coffee (Cafe Braunerhof is about a block away and still has a very local vibe; my personal favorite is Cafe Sperl, but it's maybe a mile away and outside the Ring, so may not make as much sense when you have such a short time)
-Tour the Hofburg (Imperial Apartments, Silver Collection, and Sisi Museum); if you have the time and interest, you could add on the Treasury.
-Perhaps grab a wurst as a snack from a wurstelstand on your way out of town!