Of course, the safest place would be in it's case,
in a climate controlled room, and under lock & key.

But you may argue the fact that it may not be the
best place for it.
Fine musical instruments have just as much craftsmanship put into the beauty of it's construction
as it does for it's play-abilty and tonal qualities.
And beauty is meant to be seen!
It's obvious that one wants to protect a fine expensive instrument,
but if proper discretion is used, you can have it both ways.

A personal note on displaying my guitars:

Until a few years ago, I hid my Martin D-35 away in it's case 95% of it's life since 1976,
because I felt it was
best for the guitar.
I had come to realize, that I was playing it and enjoying it much less often,
because it was just too inconvenient to pull the case out from "it's place"
and then remove it from "it's case",
every time I got the urge to play.
I also realized, that the protection the case provided,
was no longer necessary in the area where I now keep it.
Drastic humidity and temperature changes,
and wild parties, are a thing of the past.

When it is displayed in the stand,
I can visually enjoy the fact that I own a beautiful instrument.
When it's in the stand, I am confident of it's safety,
and I can easily, and quickly pick it up.
Which means that  
I play more often!
If you are as busy as most people are these days,
that can be a nice benefit.
South Mountain Woodworks