The Hofburg Palace, aka "Sisi museum" is like almost a full day, like a 9 to 5 time period. You can take an guide led tour (recommended), because there are oddities regarding every piece of art or china in the apartments, esp their personal daily habits, all of which are interesting facts about Josef and Elizabeth that aren't obvious, like her exercise habits and possible anorexia, and his once weekly bathing, 12 course dinners in 25 minutes with no talking unless the king spoke first, and seeing 16hrs a day of visitors in his logs. Family mental health issues are paramount. Note both the king and queen slept in crappy turn of the century hospital style metal frame folding twin beds so they could travel with them. Then pick up the free audio tour device.
Protip: near the very end of the self-guided audio walking museum tour, you can rushy browse through the royal china collections, which are just too numerous to have on display. Instead, head out the door a bit early and right into the library next to the exit and go through some of the GREAT travel history in display cases through the library, from some of the predecessors of the Baedecker Guides that Sisi used (she was an avid traveler through their empire and spoke something like 11 languages fluently and thus well loved by her people). There's early travel marketing print ads and other travel gear, devices and inventions.
There's something like 155 museums in Wein, so you'll have to get advice from others how long each one requires. I do recommend a half-day trip though: taking the train down to Melk, and going into the Benedictine abbey museum there which is, I believe the oldest intact european library among a great art collection, frescoed church, and a great history of Benedict and founding of his order. The gardens are gorgeous. The medieval town itself is great. Return on the Wachau Valley danube cruise, richard the lionhart ruins, and great vineyard towns.