To me, the middle one is quite natural, the other two less so. 'Settling back' implies that you are getting comfortable, and things are going well. To me, you can't necessarily predict that that will happen (things may have changed a lot since you were there) so it isn't so natural to use it in a future tense. I've just realised that there is potentially a little ambiguity there, as 'settle back' is somewhat of a phrasal verb (I settle back into my chair) but also can be two separate words, I'm going to settle, back in my hometown. (I'm going to settle there, and I'm going back). If the latter is your meaning, it would be more natural to say "I'm going back to my hometown to settle (down)".

We don't "settle back". Bad phrasal verb. We settle down into a place permanently (no intent to move again). We settle into a room/home/new town. (move in, unpack, and get comfortable) We settle up to pay off a debt. We settle on something. (decide on) So your sentence I am going to settle back into my hometown. should read I am going BACK to my hometown to SETTLE DOWN. (I am moving back to stay there permanently.)