I like to store my diamonds on my hands whenever possible.
If you are not wearing them, I recommend a safe. If you get a small safe, be sure to have it permanently installed so that it cannot be just picked up and carried out of your house.
You state that it is generally humid where you live. Your diamond is impervious to humidity. Most, if not all, Gold and Platinum alloys are also impervious to humidity. Silver may tarnish.
I also recommend getting a nice jewelry box that will keep your pieces separate from one another. This will prevent unintentional damage caused by moving the box and allowing the jewelry pieces to hit one another.
Um, you do know how diamonds are formed?
Like under extreme temperatures and pressure.
Diamonds should be stored somewhere safe from theft moreso than weather conditions.