How far is the "in a place near you" of the item "Cloak of Displacement"?

Question

The item description reads as follows:

While you wear this cloak, it projects an illusion that makes you appear to be standing in a place near your actual location, causing any creature to have disadvantage on attack rolls against you. If you take damage, the property ceases to function until the start of your next turn. This property is suppressed while you are incapacitated, restrained, or otherwise unable to move.

I am wondering how far is "near your actual location" here? Is it up to the DM to decide? If so what is their leeway?

I tried to pin it down:

• The Displacer Beast has the same description, so no help here.
• The Forgotten Realms wiki describes it as "up to 6 in (0.15 m)", but I assume it is not part of core D&D?
• As it is a rare item I assume we can expect a power level of a second-level spell like mirror image.

Answer 1

It is up to the DM

As you observe, the item does not specify this distance. This is likely because it does not matter for the purpose of the cloak's mechanical effect of imposing disadvantage on attackers, and is unlikely to matter in some other context either. In the rare situation where it does matter, the guidance from Tasha’s Cauldron of Everything (page 4) applies:

The rules of D&D cover many of the twists and turns that come up in play, but the possibilities are so vast that the rules can't cover everything. When you encounter something that the rules don't cover or if you're unsure how to interpret a rule, the DM decides how to proceed, aiming for a course that brings the most enjoyment to your whole group.

What we can infer is that the displacement should be fewer than five feet, because that is the typical space a creature occupies in combat, and if you attack the wrong space, you do not merely have disadvantage - you automatically miss.