"I will go to my father" sounds OK to my English ears. The meaning at least is clear, which is after all what counts. I'm not any sort of Eo expert, but that's exactly the problem with 'mi iras vin'. Since iri doesn't take an object, the -n must be replacing a preposition. And there's no way to know which one. I think.

Interestingly, "iras ĉe vi" is found in the Tekstaro, but it doesn't have anything to do with movement towards. It's a translation from the Old Testament, Ruth 3:16 where the English sentence "How did it go, my daughter?" is rendered "Kiel la afero iras ĉe vi, mia filino?"

Miland:Mi iros ĉe vi would be wrong

richardhall:"iras ĉe vi" is found in the Tekstaro

To eliminate the confusion, I will try to ask one question at a time.

Take a look at these sentences:
Mi iras al besto <--- Correct
Mi iras beston <--- Correct
Mi iras al vi <--- Correct
Mi iras vin <--- Incorrect. I guess this is an exception?

Alkanadi:To eliminate the confusion, I will just ask one question at a time.

Take a look at these sentences:
Mi iras al besto <--- Correct
Mi iras beston <--- Correct
Mi iras al vi <--- Correct
Mi iras vin <--- Incorrect. I guess this is an exception?

Can I just be dense for a moment? Even a sentence like Mi iras beston just seems to me completely pointless as a structure when Mi iras al la besto is standard, easy and correct.

What gain is there in thrashing all of this out? How many people are going to say: Mi iras vin? The answer seems to be: none.

Alkanadi:
Mi iras beston <--- Correct

Not so. PMEG 12.2.5 refers to names of places ending in -o, not things. The word besto does not refer to a place. and therefore we do not say Mi iras beston.

Alkanadi:You are suggesting that a preposition is required to turn the personal pronoun into a location.

I'm not suggesting anything, just saying what I observed. I've never seen in Esperanto such a thing as turning a personal pronoun into a location by means of a preposition. "Ĉe" doesn't turn "vi(n)" into a location, it simply indicates that the situation of the location is "ĉe vi", there where you are, in this case at your home. And "ĉe vin" is indicating movement toward that location where you are.

Alkanadi: 1, Why are these not equivalent?
Mi iras vin = Mi iras al vi

Same reason why this isn't equivalent in English:
I go you <> I go to/toward(s) you

Alkanadi:2, What is the different between these two sentences?
Morgaŭ mi venos ĉe vin
Morgaŭ mi venos ĉe vi

Morgaŭ mi venos en vian domon (the movement happens toward -the inside of- the location)
Morgaŭ mi venos [dum vi estas] en via domo (the movement happens inside of the location, and is not directed toward the location itself)

Alkanadi:3, Why are these sentences acceptable since there is no preposition?
...mi iris Rusujon por ekvidi...
...mi iris sudflankon de la insulo...
Sed plaĉas al Li tiuj, kiuj iras vojon pian.

Because they are locations, in a real or figurative sense.

Alkanadi:4, If people cannot be a position or direction (without a preposition to mark the x and y coordinates), then what about animals, ghosts, clouds, smoke, lightning, germs, ect..?

People (animals, ghosts, clouds, etc.) are not locations.

Alkanadi:1, Why are these not equivalent?
Mi iras vin = Mi iras al vi

[...]

3, Why are these sentences acceptable since there is no preposition?
...mi iris Rusujon por ekvidi...
...mi iris sudflankon de la insulo...
Sed plaĉas al Li tiuj, kiuj iras vojon pian.

4, If people cannot be a position or direction (without a preposition to mark the x and y coordinates), then what about animals, ghosts, clouds, smoke, lightning, germs, ect..?

Uff, I had to wait a minute in order not to use capslock. So, again:

The goal accusative can appear only with a place. A place is a either a prepositional phrase or a noun indicating a place. People, ghosts, smoke, germs... are no places. Places are places, or something else made a place by a local preposition. There ist no irregularity or inconsistency in this.
BTW: In iri vojon the accusative doesn't indicate a goal; it is the cognate accusative (interna komplemento) I've mentioned above.

Alkanadi:2, What is the different between these two sentences?
Morgaŭ mi venos ĉe vin
Morgaŭ mi venos ĉe vi

The difference is that the second sentence doesn't make sense.

Alkanadi:

Miland:
Mi iros ĉe vi would be wrong

richardhall:
"iras ĉe vi" is found in the Tekstaro

No contradiction at all, the second quote is taken totally out of context.

Alkanadi:

richardhall:"iras ĉe vi" is found in the Tekstaro

Yes, and as Richard and Kirilo81 explained, in that context it means something quite different than going to someone's place. It means something like "(How's it) going with you?"

Miland:

Alkanadi:Mi iras beston <--- Correct

Not so. PMEG 12.2.5 refers to names of places ending in -o, not things. The word besto does not refer to a place. and therefore we do not say Mi iras beston.

Thanks. I didn't know that.

Now the question is, why is it okay to say Mi iras al besto if an animal cannot be a place?

Alkanadi:why is it okay to say Mi iras al besto if an animal cannot be a place?

Because al here means towards, rather than occupying the same location as the animal.