In what state would you most likely find counties having large cities?

In the US? Every state has a pretty large city, but the largest are New York and Los Angeles (probably the biggest in land size, maybe people too, depending on how many suburbs are part of the city). So NY and CA.
Not sure why you are asking about counties, which aren't really relevant.

Eastern seaboard and then west coast. Largest Cities in the World / United States (http://www.mongabay.com/igapo/cities.htm) as you can see the biggest cities appear to be all over the place but little in the south and south west