The rule with a and an is that you use a when the word that follows it starts with a consonant sound, and you use an when the word that follows it starts with a vowel sound. You probably knew that given you used an correctly in your sentence, but I thought I'd mention that for others who may read this.
A, an and the are all articles. They're also called limiting adjectives, noun markers or noun determiners. A and an limit a noun less than the does:
"A plan."
"The plan."
In your sample sentence, you could use either a/an or the in all of the blanks, and the sentence would still be correct.
"We live in an old house near a train station. It is two miles from a city center."
"We live in the old house near the train station. It is two miles from the city center."
Both sentences are grammatically correct. The sentence that uses the is more specific about which old house, train station and city center the speaker/writer is referring to. If you were talking to someone from your city who was familiar with the area and had seen your house before (but didn't know you lived there) and had seen the train station before and knew where the city center was located, you could use the. If you were talking to someone who was completely unfamiliar with your city and the buildings in it, you would use a/an. The makes reference to specific items, and its use assumes the listener/reader has familiarity with those items.
Not to complicate matters, but you could get away with using the with city center even if the listener/reader was unfamiliar with your city. With the, you're refering to not just any city center but the specific city center corresponding to the area where the house and station are located. If that's too confusing, then ignore this last paragraph and just follow the rules outlined above.