If the power to an entire city were to be cut, would all the lights go
out simultaneously, or would they turn off in steps like you always
see in the movies and on TV?

It depends on where and how the power is cut.

What you've seen on TV and the movies is a cascading power outage.
What happens in such a case is that an overload or other problem
(which could be caused by an intentional act) results on circuit
breakers being tripped, which causes strains on other parts of the
system, which causes other circuit breakers to trip, etc.

If you look at links from the following Google searches, you'll find
many real-life examples of this happening (in some cases
intentionally, in others not):

Google search term: cascading "power outage"
://www.google.com/search?q=cascading+%22power+outage%22&hl=es&lr=&ie=UTF-8&oe=utf-8&start=10&sa=N

Google search term: "cascading blackout"
://www.google.com/search?hl=es&ie=UTF-8&oe=utf-8&q=%22cascading+blackout%22&btnG=B%C3%BAsqueda+en+Google

If, however, you were to cut off the only power source to a city,
there would be nothing to keep the lights on after the power is cut
(except, of course, for those places such as hospitals that have their
own sources of backup power).

I hope this fully answers your question.

Best wishes,

Mvguy-ga

Good answer, thank you.

You bring back memories of driving from Niagara Falls to Toronto one
night many years ago.  I was driving along the lake, with Hamilton on
my left.  Hamilton lies on a hillside, so the lights go up the hills,
making a rather interesting sight.

Along the ridge there was a large blue flash, and the whole city
turned off!!  Just like that!!!  Everything went black.  After a few
minutes, lights came on again.  Quite a sight!!  Apparently the main
feeder to the city opened.