Does the entire game take place in just one city? Doesn't this lead to a fairly stale environment by the end of the game? I enjoyed Crysis for the more diverse environments, jungle, frozen world and alien environments.

is there more diversity in Crysis 2 or is it all just "the big city"

Yes, no.
You fight in wide avenues, parks, tunnels, parking garages, various types of buildings, bridges, etc.

And of course on the surprise at the end which fits your "alien environments" request.