The Belvedere is two palaces and the slope between them, built by the man who beat the Ottomans and spent the spoils on the best garden in Vienna. It's also where Klimt's The Kiss lives. Three kilometres, mostly downhill, art at the top and quiet green at the bottom.
Start at the Upper Belvedere — Prince Eugene's show-palace, now a gallery. Do the Klimt room first, early, while it's still possible to stand in front of The Kiss without a phone in the way. Then out the garden side, where the baroque terraces cascade down past sphinxes and fountains to the Lower Belvedere, the prince's quieter quarters at the foot of the slope.
From there the walk softens. Slip east into the university's Botanischer Garten — free, labelled, almost empty, a real working collection. Then south into the Schweizergarten, an unfussy public park where Vienna just sits on benches. Quartier Belvedere station is on its edge, with Rennweg the other option if you came in from the north.
