I got a bit carried away after the third weblink that you provided above.... but had bad feelings already when adding The Vatican. The 'best fitting' ones I think are Uffizi, Hermitage, Pergamom and Louvre. Others in that category would be the British Museum, Prado, some museums in the USA (if they would be located within the boundaries of a WHS).
People now have suggested:
- Venice: Accademy Gallery
- Florence: also Bargello National Museum, Palatine Gallery and Saint Mark's Museum
- Rome: Capitoline Museums, National Roman Museum, Doria Pamphilj Gallery and National Gallery of Ancient Art