I am European and lived in America for 15 years before moving here.
I certainly understand about missing family and not having Europe on the doorstep
America is vast and you will be in one of the loveliest parts of the country. It sounds like you can choose either to live decently to well in NYC itself or in Westchester or Fairfield County, CT.
Health care is a philosophical vexation I make no excuses for, but we always had fab health care and I have no doubt that you will, also. You won’t choose to live in NYC unless you can afford good schools (a few of the state schools in the city are superb) and the suburbs have wonderful state and independent options.
Although the school shootings are too horrific for words, statistically they are akin to where air safety was a few decades ago. We used to hear about one or two big crashes a year. Did they affect our travel decisions?
There are states where the gun culture could be a concern. NY and CT are not amongst them, except that there is some hunting in upstate NY.
American exceptionalism? Yes - however, I am gently bemused that a British person does not see the irony in finding this a concern. Your informal anthem is ‘Rule Britannia’ :)
Like London, NYC is one of the world’s great cities. The two are quite different but equally wonderful. The NYC suburbs are great places for the couples and families that can afford them.
My only concern is Donald Trump, but I think the Democrats will do the right thing and prevail