Translation:My city is very big.
Town and city are, if I'm correct, somewhat interchangeable in Japanese
Town and city are very strictly defined in Japan. The name of every town, city, and village in Japan has a suffix attached denoting which type it is.
～市 (shi) city
～町 (machi) town
～村 (mura) village
But 街 (machi) can refer to any place that you live, I believe the nuance would be a place with many streets.
But do remember that there are no kanji in spoken conversations to stop confusion.
Why? I mean, I can hear it too, but why would you love the way someone pauses in a sentence?
Hometown is 故郷 (ふるさと) or 出身地 (しゅっしんち). The first tends to carry emotional content, sometimes nostalgia, as in "I miss my hometown." I think the second is more neutral or official, as in "place of origin."