"We are moving away from the city."
Translation:Elköltözünk a városból.
"Moving", here, means relocating. Giving up your home in one place and take up residence somewhere else. The Hungarian word for this is "költözni".
If the context were so that moving away would simply mean a physical motion away from the city, then the Hungarian word would be "eltávolodni". To "distance" ourselves, literally.
"Elhaladni" is not something that is used in this sense. It is rather a passing motion.
We are moving past the city. - Elhaladunk a város mellett.