Best of Baroque and Klimt's masterpiece 'The Kiss'.
My recommendation, for all first time visitors to Vienna, is to head to the beautiful baroque complex Belvedere, which consists of two imposing palaces separated by French style gardens laid out on a slope ornate with sphinx, fountains and cascades. From this vantage point the view of old Vienna has hardly changed in 250 years. Lovers of art should visit the upper gallery containing some of the best works by Schiele, Kokoschka, a fine selection of French Impressionists and the largest collection of works by Gustav Klimt. The Kiss being the most famous, although my favourite is his portrait of the young enigmatic beauty Sonja Knips.
There is one more collection that is worthy of mention here: Sculptor Franz Xaver Messerschmidt worked in Vienna at the time of Maria Theresia. For me, his collection of character heads represents the most intriguing, entertaining and funniest group of sculptures I've ever seen.
On a historical note, in the gorgeous, renovated marble hall on the first floor, the treaty giving birth to Austria's second republic, was signed by the foreign ministers of the Allied forces. And the view down to the city centre from the huge windows is quite amazing, as is the allegorical fresco on the ceiling.
At the bottom end of the park the Lower Belvedere, a much smaller palace, houses temporary exhibitions. Former owner, Prince Eugene of Savoy – modestly nicknamed “Saviour of Christianity in Europe” (because of his victories against the Ottoman Empire) lived in these chambers in summer and it shows – especially in the Golden Room, where a classic statue portrays him, allegorically, as sun god.