Mystery solved: we're all correct. "At mine" sounds absolutely bizarre to American ears, but it works just fine across the pond.
Means "at mine", "at my place".
can be the same, or "with me".
Merely means you have something in your possession, but not necessarily on your person.
So if someone says יש לך את המפתחות?
You can reply כן, אבל הן לא אצלי כרגע
Do you have the keys? Yes, but not on me right now.
Looks like many of the commenters would prefer "by me", which is not currently accepted, to "at mine". Should at least add that.
"By me" for אצלי isn't standard English, it's Yeshivish (an English sociolect.)
From Wikipedia: "The preposition 'by' has a wide array of meanings in Yeshivish […] A possible cause for this is that the Yiddish preposition 'bei' is defined as at, beside or by. The similar-sounding English preposition 'by' has come to encompass these meanings."
I wrote "The shoes are with me", and it was correct. This would be correct if you bought a new pair of shoes and someone asked where they were and you'd say, the shoes are with me. Am I the only one that thinks this is right as a native English speaker? Heh
There is really no English equivalent of "אצל", but I believe it is the same as the French "chez". Any French speakers here who can verify that?
Native French speaking here. You are right, אצל often means "chez"" in French.
Correct solution: The shoes are at mine. ??? This can only make sense in English (which I speak natively) if: 1) אצלי means 'at my place' AND 'at mine' is elliptical for 'at my place' - in answer, say, to someone saying that the shoes were at his place. -OR- 2) אצלי means 'with me' in the sense of 'in my keeping'.
Native English speaker and fluent Hebrew speaker here. I was also confused, אצלי doesn't mean 'at mine'.. i don't even know what 'at mine' is supposed to mean. אצלי means something more along the lines of the 2nd definition you wrote - i have it in my keeping. There is a difference between איתי - which means 'with me' in a more basic sense, and אצלי - which means 'with me' in the sense that you have it with you. This difference is slightly hard for me to explain, but i'll do my best. If someone is at your house, you would say they are אצלי בבית - like @airelibre suggested. If someone is simply with you - as in walking with you, you would say they are איתי. One would never say הנעליים איתי, because shoes are never simply 'with someone', they are always with someone in their keeping. The same goes for other objects - המחברת אצלו (he has the notebook/the notebook is with him), אצל מי החולצה שלי? (who has my shirt/with whom is my shirt). I hope this helped you. Good luck!
Irish people and most British people can probably draw a parallel with "on", in, for example, "Do you have the keys on you?" (It doesn't mean, on top of, rather it could be that they're in your pocket).
Native English speaking American here, who has lived in AU and NZ over the past 7 years. I associate "at mine" with British English (which would include this region) as a term, as I wouldn't imagine an American saying "The ___ are at mine" or "Let's meet at mine", though I hear (and say) it a lot after living over this way.