The Upper Belvedere hosts exhibitions of famous Austrian art, among them painters like Klimt, Schiele and Kokoschka (Visit Belvedere's Homepage - it's really great!)
The Lower Belvedere resembles Prinz Eugen's magnificent living quarters. Representational rooms like the Hall of Grotesques, Marble Gallery and Golden Room, offer a fascinating insight into Baroque interior design - JUST WONDERFUL!!!
is the man behind Schloss Belvedere, he built the Baroque juwel with the wonderful view over Vienna!
Prinz Eugen von Savoyen (1663 – 1736), one of the most prominent and successful military commanders in European history, born in Paris, but fighting for the Habsburg Monarchy against the Ottomans and many others - read more about his life at Wikipedia.
After that, walk through the Prince's splendid gardens, caress the Sphinxes :) look back over the city of Vienna, ascending the hill!