I have a nerdy wizard character that would like to create an item called the Librarians Crown, a circlet that when worn gives the user the effect of the Fox Cunning spell (level 2 spell that gives advantage on intelligence checks).

What would you say would be the rarity of such item and what cool material could she need to collect?

So a crown that gives Advantage on Intelligence checks? Or a crown that casts Fox Cunning X times per day?

Uncommon maybe.

Uncommon with attunement. Rare (maybe very rare) without attunement.

I prefer always on but x casts per day is an option for sure. It is a little like sentinel shield but for int. Arguably better for some and worse for some.

How do you guys reason around attuning? Items with activation requires and passive dont or is it just a power level thing?

The guide I heard for attuning was basically... if an item could potentially stack with stats, or if it provides an ability that effectively replaces a higher level spell, it should require attunement.

Items like this that grant advantage on a particular skill check usually require attunement, otherwise you could gather this crown, boots of elven kind, and other such items and give your character permanent advantage on all skill checks.

This isn't a particularly high level spell, and is also limited in that it only grants one of the options of enhance ability so if it simply has like... 3 charges that can be cast in a day, then it shouldn't require attunement. The only real downside at that point is the fact that it occupies the character's "head slot" for equipment.

As for what they would need to craft it... obviously they'll need a crown of some kind. Maybe just give them the requirement of "A crown worth at least 200gp", and then they'd have to collect a Fox tail, either by hunting one themselves or just buying it from a tanner. If the player wouldn't want to hunt foxes for some reason, you could also say that they need to gather a rare, magical Foxglove (a type of flower).

One shot items are definitely no attunement. After that it's pretty much a power thing. Attunement is basically a tool to control how much magic the PCs have. It's useful for making players choose which items they're going to prioritize. 

Thanks for the great insights. Just that boots of eleven kind is a non bind and so is sentinel shield. Feels like advantage on skill checks does not alone mandate attuning.

Oh weird, I wonder why I thought it required attunement. Well, it's still a bit different... this crown gives advantage to all INT based checks, while the boots only provide advantage to specifically stealth. So it would still be rarer than that, but I'm seeing now the flaws in my suggestion lol

Sentinel shield and Boots of Elvenkind only grant advantage on 1-2 kinds of check. This grants advantage on no less then 5 (plus tools). Being that the aplication is 3-6 times broader, it should have attunement or be higher rarety.

Good point[edit]. So uncommon with attunement or rare?

Depends if needs attunement. Maybe uncommon, if needs, or rare if doesnt need.