I don’t have experience of Long Island or New Jersey but those are both big/general areas. It’s like saying what’s Surrey like when you know one part of Surrey is very different to others.
Id avoid anything further than 45 minutes by train if you can help it - the commute can be tedious, particularly if you have to add a subway or cab journey once you get to the city.
Please don’t underestimate how much more money you will need here to maintain your U.K. lifestyle.
Get your DH to get a recommendation of a couple of realtors from one of his colleagues while he is here and start meeting them, even if only by zoom. You won’t be able to do anything with out one.
to help you work out which areas you want to focus on, look at you tube for drive throughs or realor videos like this one. You’ll get a feel for some of the areas
compare the slick and shiny realtor videos with a drive around filmed by ordinary people to give yourself a balanced view.
Personally, I’m a fan of Larchmont, its central parts are unusually walkable for the US - you might even be able to get away with one car. But rental housing can be rare and expensive for what you get - look at the Trulia app. As well as Zillow.
in terms of meeting people, try to get a house with a front porch or spend time in your front yard “gardening”. Your neighbours will introduce themselves if you’re visible. your kids will also provide an instant network if you’re in the suburbs.