My honest opinion is that Cup banners, conference championship banners, divisional championship banners, and retired numbers should be the only things that hang from the rafters. Anything else, including Presidents' Trophies, should not be up there, especially as if you fail to win the Stanley Cup a PT banner would just be a constant reminder that your team underachieved when push came to shove when it really mattered, and the Cup banners and retired #s are the only things that warrant ceremonies while you raise them.
*10 years from now*
Dad: See that, son? That's a Presidents' Trophy banner. We had the best record that year.
Son: How'd we do in the playoffs that year?
Dad: *screams internally*