Why does Kyoko come to the city in Madoka Magica? Why does Kyoko come to the city in Madoka Magica? 

There is probably a very simple answer for this, but I'm too lazy to go back and rewatch or to skim through a wiki.
Why does Kyoko come to the city?


We learn quite a bit about this in The Different Story, a sidestory manga that basically tells us about Kyouko and Mami prior to the events of the series (mostly before the point where Homura wakes up in the hospital, meaning that most of what we learn is timeline-agnostic).

There is an informal system among magical girls whereby each one has their own "territory", so to speak, within which they and they alone can hunt witches. This is because having multiple magical girls work together in a given area requires them to split the proceeds (the Grief Seeds) amongst each other, which nobody really wants to do. 

Upon learning that Mami has perished, Kyouko ― who, until that point, had the neighboring city of Kazamino as her territory ― presumably saw this as a good opportunity for her to expand her range.