Looking for something to reference in a character background. PHB says some of their cities fade in and out of 'this world' on a daily cycle. Ideally somewhere feasibly accessible to Nentir Vale, but beggars can't be choosers.
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You know as much as we do – as covered in this question, the setting was never detailed more than the loose sketch provided in the PHB. As mentioned, there were a few adventures that were set in specific places and in that way added slightly to the setting, but the overall geography and population information was never expanded on.
This is both a feature and a bug. It's a feature because it's intended that DMs could create as much material as they wanted without contradicting anything "official". It's a bug because players like you who want official detail don't get any support.
Ask your DM to make up an Eladrin city and put it somewhere suitable for your character to hail from.