Does anyone know of a website or resource that identifies the nearest journal neighbours to journal X (any specific journal) in terms of content (perhaps defined by some distance metric defined on article keywords?). In other words, if I am rejected by journal X, which journals might consider the same paper?
Indeed, there are tools that create maps of journals in a given area. Most of them are based on citation data, i.e. they consider that citations between articles of journal A and journal B are a good indicator of proximity of the two journals (and it seems like a good definition of “proximity”). If you are interested in the topic of how such maps are created, and how they can be analyzed, you can read on the topic. For example, see “Seed journal citation network maps: A method based on network theory” and related papers.
A final note: while such journal maps can be useful in discovering new journals in a field you don't know well, I will add that each journal is unique, and you have to learn about the journals in your field in order to increase your chances of success at publishing articles. It may, for example, tell you that two journals are very close in scope when they actually have very different editorial policies. Read the editorial guidelines for the journals of your field and, at least as importantly, read papers of each journal to get a feeling of what the actual policy in place are.
If your institution has access to Journal Citation Reports, there is a feature called Related Journals that will provide a list of titles similar to your selected title, based on citing and cited relationships. Journal Citation Reports is a subscription database provided by Thomson Reuters