Some people, often rather militant opponents of prescriptivism, say that there's a difference between 'deciding not to P' and "deciding to 'not P'". They would say that if you mean 'their decision to not go' you should say that, in defiance of the many teachers who would forbid it. 'When I split an infinitive, I split it so that it stays split' [that's a bowdlerized version of the original Raymond Chandler(?)]
In those cases, I try to use a verb that includes a negative - like 'forbid', 'veto', 'ban', 'abjure', 'deny', 'abstain...'. So that rather than 'He decided not to eat' I would say 'he decided to fast' (so that nobody could complain about where I'd put the 'not' ). But there isn't a suitable negative-loaded opposite to 'go': 'He decided to avoid Vladivostok' is a bit extreme - it suggests there's something frightful or ghastly or heinous or dangerous there. 'He decided to give Vladivostok a miss' would be OK, but quite informal.
You could say 'He decided against going', or use some other verb - 'He ruled out...', 'He dismissed the idea of...) - this one is quite useful, because you can qualify the dismissal: 'He dismissed as ridiculous/impossible/fanciful/self-indulgent... <whatever> the idea of going'. But as I said at the beginning - and as someone will probably have already said before I hit the Post button - your version is fine.
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