What does the bolded phrase mean in the following:
"Maybe you will come to London sometime."
How is it different from "You should come to London sometime."?
I don't know that there is much difference between the two. In his comment Hank suggests that "Maybe you will ..." can be a kind of invitation, but I think this depends more on context than anything else.
London is a beautiful city. Maybe you will visit it sometime.
This is just a recommendation, not really any different from "you should visit London". The difference between this and your example is the direction of the verb. Because I'm saying "come to" someplace, it implies that I live in London, and I'm inviting you to visit. "You should come to London" can be a similar invitation.
However, not necessarily a formal invitation. As Hank mentions, if it is phrased as a question it more strongly implies invitation, but otherwise you really should clarify and confirm before making the trip.
Of course I know some people who would go anyway and just "show up on someone's doorstep", claiming "Hey you said I should come sometime!" But that's more about personality and culture than about English.
Without further context, both "Maybe you will come… " and "You should come to London…" are both suggestions that the listener(s) might visit London. They might be invitations, but that's by no means necessarily so.
Where they differ is in strength. "Maybe you will… " is perhaps vague speculation while "You should…" might well be a recommendation