I hate to possibly be the bearer of bad news, but I can’t think of any plot points in that movie that involved Vladivostok. The action all took place in the Barents Sea and North Atlantic, after Red October left Murmansk through the Polyarnny Inlet. Vladivostok is on the other side of the country, many, many time zones away.
I wonder if there is a reference later in the movie? Either that or it was another movie and the reference was about sending you to the middle of no where, because, as you said, it’s out there.