Translation:My city is a few kilometers from the coast.
As a native English speaker, I sure that "My city is at some kilometers from the coast." is acceptable. In the UK we might say "My city is at some miles from the coast"
"some" does not automatically signify "few" or "many", it signifies an unspecified amount greater than zero or perhaps one.
It's because the speaker is not putting any separation between the adjacent stressed and unstressed phenomes, rather just ever so slightly elongating the sound, which is extremely common among native speakers. It's known as connected speech and it happens in every language, although the specific forms it takes differ.
For example, in English, take the sentence "Give me an apple". If you think about how it sounds pronounced slowly and independently you'll surely notice it isn't the same as how it's actually said in normal speed speech, which is more like "Gimme uhnapple".
Another example, this time in Spanish, is instead of saying «Está al sur» as three distinct words, most native speakers will actually say «Estál sur». In the case of this sentence «está a algunos» becomes «está_algunos».
I disagree. "Some" can indicate, quite a few, depending on the context. Consider the following quote from Melville's Moby Dick.
"Some years ago - never mind how long precisely - having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world..."
As a native English speaker, I think that "My city is some kilometers from the coast." is acceptable. However I think a better and more natural way of saying this would be, "My city is kilometers from the coast." It is implied that it is some unspecified distance away. But you shouldn't need to include "some". Right now if you leave out "some", it marks the sentence as incorrect. They should fix this.