Translation:I am from Tokyo.
Agreed, 故郷 (ふるさと) also carries that same meaning.
However, at OP, I think "Tokyo is my hometown" puts the emphasis on "Tokyo" in a way that 東京出身です and "I'm from Tokyo" do not. 出身 means "a person's origin", so the emphasis remains on the person. Arguably, it's not a big difference, but it's there nonetheless.
This is a great question, and there isn't really a simple answer. For some reason or another, Japanese people tend to write either:
- always using the relevant kanji, like 来ます, or
- always using the hiragana, like (時間が)かかります instead of 掛かります, or
- for some words, such as 達/たち or 子供/子ども/こども, it varies depending on the person and/or the context.
In that sense, we simply learn whether to use the kanji or not based on repeated exposure to the "correct" way. It might feel a bit too early for you at this stage, but this is the start of the process. Personally, I think it's never too early, so in my other comments, I try to include normal kanji usage (with hiragana for pronunciation) as much as I can, except when the thread I'm commenting in has already stuck to the way Duo has taught it or I forget.
As for why this happens, even my Japanese partner doesn't know how to explain it, but there are a couple of advantages to it that we thought of. Bear in mind that we're not a linguistics experts though, so the complete explanation may be due to some combination of these and other reasons.
The first and most simple is to avoid confusion between homonyms. I'll take きます as an example here: it can be "to come" (来ます) or "to wear" (着ます). But that isn't the full picture.
Another consideration is to maintain consistency in verb conjugations, making sentences easier to parse. I'll use 来ます as an example this time because it's a fun irregular verb:
- 来る (くる), plain present tense "come"
- 来た (きた), plain past tense "came"
- 来ない (こない), negative plain present tense "don't come"
As you can see, the pronunciation changes depending on which form of the verb you use, but by using kanji, it's immediately obvious they are related words. (One counter example to this is the verb する "to do" which changes pronunciation too, but it is rarely written using its kanji 為る.)
Speaking of making things easier to parse, using kanji in the verb makes it easier to get meaning out of other words. For example, we know 来ます means "to come" but 着ます does not, so we can infer that the kanji 来 is associated with the idea of "coming". If I then told you that 年 means "year", could you guess what 来年 means? It means "next year", in other words "the coming year" ;) the pronunciation is completely different (らいねん), but that's a story for another time... f(^_^;
The relationship between the kanji and the meaning isn't always this straightforward; for example, 来日 (らいにち) doesn't mean "tomorrow", but rather "to come to Japan (日本)". But in principle, having kanji helps you figure out where one word ends and where another starts. For beginners, it might be more difficult than helpful, but once you build up a bank of kanji, it makes learning new vocabulary and reading much much easier.
This comment is already getting long, but let me just show you how much easier reading with kanji is. Take the sentence in this exercise: とうきょうしゅっしんです
Just read the first 2 characters: とう. What does it mean? Without any context, can you even begin to guess what the sentence might be talking about? To me, とう could be 当, 投, 登, 搭, 到 or more kanji depending on what else comes next. I don't even know if とう represents one word or not; う could be the start of the next word.
On the other hand, if it was written in kanji: 東京出身です The first 2 characters are 東京, and immediately this gives us a lot more information. 東 means "east", so straightaway, we can guess it's talking about a location, even if we didn't immediately recognize the place name. 京 means "capital", so by putting it together with 東, we get the eastern capital of Japan, i.e. Tokyo.
Granted, you're going to need a lot of kanji knowledge before this sort of reading is faster than reading hiragana, but Japanese people have a lot of kanji knowledge, so they like to use this system which means we, as Japanese learners, have to eventually learn it too ;) 頑張ってね (がんばってね)
Plus with kanji you can infer meanings in situations where you don't necessarily know how to pronounce the words.
For example 今日, if you knew the 2 kanji used then you could tell that it means today even if you have never seen that combination before. The first one is now the second is day, and if you knew that then you could get the meaning today even though you have never seen it before.
Bonus points if you already know the word きょう because then you can literally read it instead of just getting what it means.
Was that in a written or audio exercise? I could be wrong, but I think "My answer should be accepted" is an option with written exercises, but NOT audio ones.
There is a problem with the Japanese audio exercises though. It seems that there is only one "right" way to write an answer when doing an audio exercise. I have been marked wrong (quite unfairly) numerous times for using kanji in an audio exercise. But when I substituted hiragana characters for the exact same word, I was marked correct.
With written exercises, on the other hand, there is more flexibility and both hiragana/katakana and kanji alternatives are usually accepted in those. At least, that's been my experience of this course to date. I certainly feel your pain though.
"I come from Tokyo" would indicate you are travelling. Say you got on a train and someone asked you where you had got on the train. You could say "I come from Tokyo." But "I am from Tokyo" indicates a place of origin. You started in Tokyo at the very start of your birth, so you are from Tokyo. I hope this helped :)