As for your example, **It makes me think of home.**

It sounds like you have a lucid image of hometown, therefore you can say **故郷が思い浮かぶ**.

On the other hand, **故郷が浮かぶ** sounds like images just simply pop up in your head and it's not so important or you have a vague image of hometown. Since **浮かぶ** connotates with an expression like **雑念が浮かぶ: miscellaneous thought comes into mind.** which are unstable images. Therefore, in my opinion, **故郷が思い浮かぶ** sounds you are retrospecting your hometown rather than saying **故郷が浮かぶ**.