Month nine to fifteen is the wall. It is common enough that I now warn people about it in advance, and almost nobody believes me until it happens to them.
What it usually means is not that you want to go home, it is that novelty has stopped paying for itself. Early on the newness of a place is a reward in its own right. After a year your brain has recalibrated, a new city is just a city, and now you are paying full price in logistics for something that no longer feels like a treat.
The fix that works for most people is slowing down rather than stopping. Pick somewhere you already liked, take a six month lease, unpack completely, and put one thing in your week that repeats: a class, a team, a Tuesday. The dread lifts within a month or so. Several people I know made an expensive decision to quit entirely at month thirteen, and what they actually needed was to stop moving for a while.