Storage that does not look like storage
The question is not where to put it. It is who might open it. Once you name the actual audience, the answer stops being a matter of taste and becomes fairly narrow.
Name the audience first
A guest. Someone staying over, a family member, a cleaner. They open cupboards looking for a towel or a spare phone charger. They are not looking for this, and if they find it they will be as embarrassed as you are.
A partner who does not know. Different problem, and not solvable with a box.
A child. This is the one that actually decides the design. A seven-year-old opens everything, does not know what they have found, and will either ask you about it in front of other people or take it to show someone. There is no version of that which is fine.
Most people plan for the first and forget the third, which is why the drawer stops working at exactly the point it matters.
Three levels, and what each one actually stops
A drawer stops nobody. It is not storage, it is deferral.
A plain box — an unmarked container, a wash bag, a shoebox — stops a guest, because a guest looking for a towel will not open a random box in a wardrobe. It stops nobody who is actively curious.
A lockable case is the only thing that works against a child, and children are the realistic threat. Not burglars, not the police, not anyone dramatic. A seven-year-old with an afternoon and no supervision.
If there is a child in the house, this is not a preference. It is the only category that answers the question.
The conflict nobody mentions
The place people hide things is the bathroom cabinet, and the bathroom is the worst room in the house for the object itself.
It is the warmest room for part of the day and the dampest all of the time, which is precisely the combination that accelerates plasticiser loss in soft materials and grows things in anything porous. It is also the room guests use.
So the two goals — hidden, and stored well — point at different rooms. A wardrobe shelf is boring and correct. A bathroom cabinet is convenient and wrong, and the damage takes about six months to show.
What to avoid
Branded packaging. A box with a photograph of the product on it is the opposite of discreet, and it is also usually the type with a moulded plastic window, which is often PVC and will interact with anything soft stored against it.
Anything that rattles. A hard case with loose contents announces itself when moved. Foam, or a fabric pouch inside the case, fixes this for almost nothing.
Anything that looks expensive. A nice-looking box invites a look. A dull one does not.
A pouch that says "discreet" on it. This exists. It defeats itself.
Airtight is the wrong question
Sealed containers are fine for something that is completely dry. They are a mould incubator for something that is not.
So the sequence is: wash, dry with a towel, leave it out for an hour or a day depending on whether it has a motor and a seam, then put it away. A sealed case is then the better choice because it also keeps dust and lint off, and dust on a soft surface is a large part of what people describe as "it feels horrible now".
The trade-off worth naming
Storage that is hard to get to is storage that does not get used.
A case at the back of a cupboard behind two boxes is more private and worse. A case on a wardrobe shelf that takes four seconds to open is less private and better. The point of owning it is using it, and the friction you add to protect it is friction you also add to using it.
The reasonable compromise is a lockable case that lives somewhere you can reach without moving anything, which almost always means a shelf rather than a floor or a loft.
Questions that come up
Are lockable cases worth it?
If there is a child in the house, yes, and nothing else substitutes. If there is not, a plain box does the same job for less.
Is a makeup bag fine?
For a guest, yes. Check the lining: woven fabric is fine, the shiny coated kind is a plastic film and will interact with anything soft stored against it.
Do I need a safe?
No. A safe is heavier, more obvious and more expensive than the problem requires.
Should it be airtight?
Only once the contents are properly dry. Before that it is the worst option available.
What about the box it came in?
Usually fine if it is rigid with a foam insert, and usually not if it has a clear plastic window. It is also, by definition, not discreet.
More guides
Where to store it
The drawer next to your other things is the single most common way a good toy gets ruined, and the damage is invisible until you take it out six months later. Four things do it, and only one of them is about the toy itself.
Why it went tacky
A sticky surface gets blamed on bad cleaning almost every time. It is usually the material, and there are three different reasons for it. Only one of them is fixable, and telling them apart takes two days.
How to actually clean one
Most cleaning advice for these products is either too vague to act on or quietly wrong about the materials. The part that matters is knowing which of two categories yours falls into, because the two need different things and one of them cannot be sterilised at all.