This is the winter palace of the Habsburg family. Closely modelled on Versailles in Paris, it sports large, beautiful gardens and poses in a striking yellow colour. It's been recognised since 1996 by being placed on the UNESCO World Cultural Heritage List.
We took the "grand tour" of some 40 state rooms when we visited. This was a self-guided audio tour available in many languages and was fascinating. It gave a real insight into the Habsburg family, more so than the static displays at the Hofburg (see other journal entry).
It's surprisingly close to central Vienna, an easy 20- or 30-minute ride on the underground, and definitely worth a visit. Be warned! It's quite a climb up to the top of the gardens, but this yields a picture-postcard view of the whole palace.
The palace's website can be found at http://www.schoenbrunn.at/