Perhaps you mean 'Birthplace' instead of Birthday town? Birthplace is where you were born. Hometown is where you grew up. Not always the same place. I was born in Honolulu but grew up in Kaneohe.

If someone asked you what your hometown was, you would usually think of the place where you spent the most time growing up - the place with the most memories (good or bad). Your birthday town is just the place where you were born. Since most hospitals aren't located in small towns, it might very well be that the place where you were born is not where you grew up. Indeed, you might very well not have any memories of your birth place at all.

'Hometown' leads us to some very nice words in modern english slang. Originally part of southern californian black dialect, they are now adopted all over the country, especially by young people. Like mahy slang expressions it's best if you don't overuse it, but it's nice to know about it: "Homeboy" someone from your hometown. Hence also 'Homegirl' And this leads to the most colloquial: "Homie" Hey Homie! Whassup? (Hey neighbor, what's up (new)?) And this has led to another version: Holmes, like Sherlock Holmes the detective. It's jsut silly wordplay, but I like it because it's affectionate and warm: "Nice work Holmes!" Your listener might need to be young or hip to understand, though.

Oops, I messed up. Derrick is right. You would never hear the term "Birthday town" by a native English speaker. Use "birth place" instead.