One little factoid which hasn't been posted yet, but may help sort out the OP's bewilderment: legal fictions aside, Tokyo, Kawasaki and Yokohama are not separate "cities", they're just labels for parts of a vast urban sprawl. If you ride from one to another on a train, there's absolutely no way to tell where one ends and the other begins. Kawasaki, in particular, is an utterly anonymous 'there is no there there' jumble of suburban housing and small factories, with nothing approaching a 'center'.

As a more graphic demonstration, take a look at this:
http://maps.google.com/maps?q=tokyo&...1.115456&hl=en

Highway "1" is just west of Yokohama. Kawasaki is right about under the "15" and the top center blob is central Tokyo. Now zoom about a couple of stops to here:

http://maps.google.com/maps?q=tokyo&...1.115456&hl=en

And try to imagine that everything in white on the map is covered in concrete. (Google Earth will do an even nicer job of hammering the point home.)