Which is the correct usage when I tell someone that I am back?
I am back to [some city]
I am back in [some city]
FumbleFingers comment on EdGuiness answer is, I think, the real answer. When you are describing a destination, using a verb such as "go", you use the preposition "to". When you are describing a "state of being", using a verb such as "to be", you use the preposition "in".
Note that if you do use a non-proper noun like "city" or "town", you need to include an article.
Side note: "Town" without an article has a varity of special meanings. "I live in town" means that I live within the city limits, as in:
"I am/was/will be in town" means that I am in the city under discussion as opposed to travelling somewhere else. Like:
"We went to town" can mean that we went to the city under discussion, but it is also a slang term meaning we had a wild party or had sexual relations.
The correct usage is "I am back in [some city]".
The word "to" does not work with the verb "to be" in this context, since it's used as a preposition that means "toward" or "in the direction of".
You cannot be to a location, but you can go to a location, as examples from other answers show.
The word "back" should fit in there in a way that it would still be Ok even if it was removed:
I am to the city. = X
I am in the city. = Ok
I have come to the city. = Ok
I have gone to the city. = Ok
We then return "back" and we have:
I am back to the city. = X
I am back in the city. = Ok
I have come back to the city. = Ok
I have gone back to the city. = Ok
I went to Melbourne to visit my old chess club.
Now I am back in London, where it is raining.
Some time soon I will go to Brisbane for the sunshine. (It's too hot there, for chess)
And then after Brisbane, I will come back to London, to the rain.