What is a Latin phrase to express the sense of belonging to a particular place? How can this be translated from English to Latin?
I suggest the word adjective localis. It is not exactly the same as the English "local", but evidently related to it.
Lewis & Short translates it as "of or belonging to a place, local". Some use examples are mentioned in the linked dictionary entry, including adverbia localia ("adverbs of place", Scaurus, De Adverbio et Praepositione 29.8) and localiter ("locally" or "by local inhabitants").
As always, the best translation depends on context, but the adjective localis is my best first guess for "belonging to some place".
Or did you perhaps mean phrases like "I was born here and I belong in this city"? That would be a completely different story.