Thanks @Astorian31!
I'm in the services-management department and the NYC gig comes with much greater responsibility, and the references/recommendations part has been taken care of. So while there is a scope for negotiations, you're right about being realistic!
I would like to live in Manhattan for some time but my wife suggests NJ as living in the City might be too costly for us (we don't have kids). I've been doing a bunch of internet research to make my case and to change the verdict.
Let's see how it goes.