Valuable Items, conversely referred to more colloquially as junk items, are sellable items that can turned into Item Maniacs for lucrative payouts of Pokémoney.
They are generally functionless items that exist strictly for their sellability as another avenue for money-making in this game; the only anomaly is Stardust, which is instrumental for some tasks in the daycare-task quests and thus is the only sellable item herein that is buyable.
Kanto's iteration of the Item Maniac in his Route 25 house.
These items can be sold to any of the one-per-region Item Maniacs for the prices noted above. They can be sold either all at once or in increments of 1 per transaction.
Item Maniacs can be found stationed at the following region-respective areas:
Kanto - the Item Maniac's residential house on Route 25.
In the Sinnoh Underground daily quest, Tiny Mushrooms and Stardust are potentially required items for hints on finding on the Treasure Room.
One can exchange 10 Mirror Shards for a Reveal Glass at the Wondrous Site, which can be used to transform Landorus, Tornadus and Thundurus into their respective Therian form.