So finally we are assuming the definite article. How am I supposed to know when to write "the" in front of the noun for the subsequent modules?
Here the word "place" is modified ("restricted") by a following clause ("that I come from"). In such situations, English uses the definite article "the" before the noun that is so modified. So, in such English sentences (where a restrictiing clause follows the noun), you should insert "the" into your translations from the Czech.
But note, this is a peculiarity of English, not of Czech.
I agree with Christine, 'the place where I come from' is natural in American English at least. 'The place which I come from,' which the program suggested as the correct answer, is not grammatical in English.