Tehran city OR Tehran City? Or maybe the Tehran City? Which one is grammatically correct?
...or indeed 'Mexico City' and several others. They usually (always?) have the word City capitalized to distinguish them from some other organizational entity: New York City is distinct from the state of New York, Mexico City is distinct from the country Mexico...
So if I want to bring 'city' after 'Tehran' can I say 'Tehran city?'
Why would you want to?
If you insist on using 'city', you could say 'The city of Tehran', as tedmc pointed out.
There is no reason to. It's just called Tehran. You might qualify it in advance by saying "the city of Tehran" or "the city, Tehran" depending on context. However, as usual, we would need a complete sentence to work with.
(Cross-posted with Rover.)
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Who's your audience? Many will know the city and not the province, so it would be unnecessary. However, I would still use the city of Tehran if you needed to make the distinction, but I would be more likely to make the distinction for the province rather than the city.
As an example, if someone says Washington, I assume they are referring to Washington DC, not the State of Washington, simply because we talk far more about the city than the state.