You didn't mention the length of your stay.

My answer is see everything...this property, IIRC, is centrally located - Hofburg, Spanish Riding School, and the list goes on. You will not go hungry either. Vienna is a beautiful city!

Because of my own interests, I'd note the Vienna Fire Department museum, located very close to the Hofburg. It is likely the best fire museum that I've visited. And Vienna can claim the first organized fire department in the world.