"I'm not use to this city life" OR "I'm not used to this city life" ?
The adjectival phrase "used to" is invariable: it cannot take the form "use to", even in questions ("Are you used to that?").
There is a verbal form which is similar, and may be confusing you. In current English, this phrasal verb also takes the form "used to", because it exists only in the past (it could be used in other tenses a couple of hundred years ago, but not today). But in the negative and interrogative it is "didn't use to" and "did you use to?".
Because the 'd' of "used" and the 't'" of "to" are homorganic, they are usually run together as effectively one word; so some people are unsure whether to spell it "use to" or "used to" (John Lawler treats it as one word and writes "useta") But traditionally it is always "used to" except in the cases I mentioned.
In your sentence, 'used to' is an adjectival phrase.
I'm not used to getting up so early.
Used as an adjective can also mean something that isn't new:
I only buy used cars. New cars are too expensive.
I use a dictionary to learn new words. (verb)
Another use for a dictionary is learning how a word is pronounced. (noun)
Another confusing thing about use is that "used to" is a modal verb meaning something that has happened continuously or frequently in the past.
I used to live in New York, but I moved to Texas.
It is easy to confused "used to" the modal verb with "used to" the adjectival phrase. It's important to look at the meaning of the sentence to see which one makes more sense.