没有 as an answer. Cannot be 不?。
A:你家住在哪里? 还住在城里? 


Both 没有 and 不 denote negative, B is replying to latter part of the  question "还住在城里嗎?" B's reply would either be positive or negative. And he doesn't need to repeat A's question in his answer, so he could simply answer:

"不"(meaning 不是住在城里) 

or 

"没有" (meaning 没有住在城里)

"我们最近搬到郊外住了" is not a part of the answer but an additional explanation

Notice "还住在城里嗎?" is a question asking for confirmation of positive or negative, so you can simply reply with a negative "不/ 不是 /没有", or a positive "是"

However, if the question is specifically asking "是不是" or "有没有', you have to answer specifically with "是/ 不是" or "有/ 没有" 

Example: 

A: "有沒有工作?"

B: "有" (you cannot reply with "是")

B: "沒有" (you cannot reply with "不是")

~

A: "是不是你?"

B: "是" (you cannot reply with "有")

B: "不是" (you cannot reply with "沒有")

Also: reply with the verb used in the question

A: 去不去玩?

B: 去 (you cannot reply with "有去")

B: 不/ 不去 (you cannot reply with "沒/ 沒去")