The video was shot before Communism ended, which means the police officers you see are dressed as soldiers, the wall at the Old Jewish Cemetery is in disrepair, the Charles Bridge is virtually empty, and Old Town Square has plenty of tourists but no stands geared toward selling substandard crap to tourists. But you still get to see Prague in all its beauty; I'd even argue that the cold, gray skies add to the romance rather than detract from it. Or maybe that's just the pitch-perfect, wouldn't-change-a-note-of-it sax solo.
All of Prague's standard sights are here: the view of Prague Castle looming over Old Town, the walkway leading to the castle where you get a view of St. Nicholas Cathedral and the rest of Mala Strana, Charles Bridge, a night shot of the National Theater, the astronomical clock and Old Town Square, and the banks of the Vltava where one can feed swans, take photos and, apparently, play the violin. I don't have a blow-by-blow account of which landmark appears when, but luckily this map done in 2008 does.
And now, your tour of Prague, courtesy of INXS.
UPDATE: For those who can't see the video, there may be some copyright-country thingy preventing you from seeing it, depending on where you are. Typing "Never Tear Us Apart INXS" into your YouTube browser should do the trick.