Another of Vienna's main sights - A collection of Austrian art (including much of Klimt's work), in the grandest of surroundings. The manicured gardens are free to walk through.
Entry to the upper palace (for the bulk of the art) = €14 (11.50 for students)
Getting there: Take tram 18 (direction 'Schlachthausgasse') from Westbahnhof station. Takes about 20 minutes. Get off at 'Quartier Belvedere'.