Think of the difference between any and every.
any adj 1
1. one, no matter which • can't find any answer.
2. some, no matter which • have you any apples?
[other definitions omitted]
every adj 2
1. each one or single of a number or collection; omitting none.
[other definitions omitted]
any 3
2. used to refer to a person or thing of a particular type when what you are saying is true of all people or things of that type:
- Any child who breaks the rules will be punished.
- Always check the details carefully before you sign any written agreement.
- I can see you any time on Monday.
- If I can help in any way, let me know.
[other definitions omitted]
every 4
1. used to refer to all the people or things in a particular group or all the parts of something:
- We looked carefully at every car that drove past.
- Every child will receive a certificate at the end of the course.
- I enjoyed every minute of the film.
- I listened carefully to every word he said.
[other definitions omitted]
In general terms:
- any is referring to one or more items, people, or places individually
- every is referring to all items, people, or places collectively
So you can then apply those prefixes to get the words anywhere, everywhere - anyone, everyone, with the prefixes carrying over their individual meanings. Hence:
- everywhere = all places
- anywhere = one or more places
Therefore, when searching for something, you might say:
- I looked everywhere, ... = I looked in all places
- ... but I couldn't find it anywhere = I could not find it in any one of the places I looked; I found it in not one (none) of the places.
If you had said "I couldn't find it everywhere", it would have meant "I could not find it in all places (but I did find it in some places)."
So if you have lost a particular item, you look in all places (everywhere), with the hope of finding it in one of the places (anywhere).
In a different situation, such as in a busy city, you might say:
- "There are cars and people everywhere: there is nowhere that is quiet."
nowhere = not anywhere
Going back to your original question:
- I would say that you "use anywhere" when you are referring to a single place, the location of which is immaterial (doesn't matter). [I'm avoiding using "important" because that can have other meanings.]
- You are correct in suggesting that "anywhere" is often used in a negative clause; e.g. "I couldn't find it anywhere"
- and also that "anywhere" is often used in a question; e.g. "Is there anywhere (any one place) that I could get a coffee?"
Before answering this question, I looked for any previous questions that had addressed this issue. I couldn't find any, but I did find several previous questions that discussed anyone & everyone. You may find some of those useful:
This previous question may also be of interest (although it doesn't discuss the word anywhere):