Is the oath sworn by the questioner in a state of anger, without intending to visit a certain city again, considered a binding oath or a vain oath (laghw)?

If you swear an oath unintentionally, it is considered a 'laghw' (idle oath) for which there is no expiation. This is like saying "no, by Allah" or "yes, by Allah" which may slip from the tongue without intent. The proof for this is Allah's saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths" and His saying: "but He will impose blame upon you for what your hearts have earned."