A few definitions:
permanent - not permanent on the scale of the Earth's lifetime, but good enough to last a couple hundred years - seeming permanent to those who were born there at least.
size of New York City - roughly 305 square miles (491 kilometers)
fog - should consist of water, goal is to achieve visibility below 100 meters (109 yards) while preferably staying around 30 meters (33 yards).
what location? - preferably midwest U.S. but whatever location you need in order to make it work, so long as the land-covered area stays at 305 square miles or larger.
What human-induced disaster could cause permanent fog in an area the size of New York City or larger?