Hi, I live in NY and was in NYC for 5 years before moving out to the burbs of NY.
I'd say that $90k is really low for a family of 4; a lot of your costs will be rent, groceries and utilities. If you get subsidized rent from DH employer then check where it is, as this will drive where your kids go o school. The rule of thumb is usually 'better' school areas drive the rent prices up. You could live further out but then need to check the commute for your DH as getting to the UES if you have to cross the city horizontally or up from Brooklyn is a pita
Groceries are high cost- there's no tesco express or similar driving economies of scale for purchasing, especially if you live in / around the city. For a family of 3 I usually spend on average $180 -$200 a week (includes cleaning stuff and laundry stuff) and that's shopping around at the cheapest places. We do eat meat but I do budget
Utilities (phones, electric etc) are also high compared to the UK as there minimal competition. I've also found kids stuff more expensive - so clothes, activities etc. Kids classes (gymnastics or whatever) usually come in ~$30+ upwards a session, and I never really found anything that was equivalent to a cheap / good drop in like you get in the UK. BUT this depends on area - the UES is v family friendly and you're right by the park and you're not far from the major museums etc
Imo, its way more expensive than the UK and London, and thats before factoring in flights home etc
Health insurance is probably the big one; atm you shouldn't be excluded from cover because of your son (they can't refuse for pre-existing conditions under Obama care, don't know how long that will last..) As well as checking what your employer provides you need to check what the excess you'd pay would be
We've just chose our insurance plan for next year; we get good provision (employer pays ~78% of the costs as subsidy) Our choice of the 4 plans they offer was based on how ill we may be / any known surgery coming up plus how we cover any shortfall in costs
Our insurance cost per month is $550 pre tax, which covers health, dental and vision. Our costs are pro rated based on salary, so the higher take home pay the higher you pay, but its relative to pay. On top of this $550 we have to pay the first $6k a year in excess; once we reach the $6k there's a sliding scale of what else we have to pay - preventative stuff (screening etc) I think its $0, the other stuff (A&E admission, consultant visit etc) we have to pay the first 20% of costs
Everyones plan / costs will be different depending on situation, but I can safely safe its one of our largest costs. On the flip side, coverage is excellent (again, will depend on your plan...) and there's never any quibble about tests, X-rays, no waits to see the Dr etc
Irt services for your kid, NYS actually has good mandated provision for services such as speech therapy, 1:1 assistants in classrooms etc for free,, am happy to provide info if thats relevant for you as we get services in school for our kid (who's also 4)
I'd also factor in the costs of keeping your UK house and renting it out. I kept my UK place and rent it out - I keep 1/3 - 1/2 of what I get in rent for it aside as every year without fail there's been repairs needed!