The train ride from Harrison to Grand Central alone is somewhere around 45 minutes. And unless you work right at Grand Central, you're looking at rushing to make connecting trains. Doing this for a week while exploring the city was fine, but the idea of having to do this every single day until I retire just to make a living would make me want to blow my brains out.
I don't know how my cousin does it. She works in the financial district and takes a 6am train into the city every day. When she gets home, she has just enough time to put her kids to bed before passing out. Now I understand why her husband has a WFH job.
And about that "great family home" thing... the housing stock is so old that every house, even the nice ones, is going to be a fixer-upper. Not long before I got there, they had a plumbing joint break in one of the upstairs bathrooms. Within a few minutes, it wrecked the fixtures in that bathroom, obliterated the ceiling of the kitchen it was above, and did a number on the kitchen counters.
I'm also generally not a fan of how the suburbs are laid out either. Houses are spaced so far apart that it feels like you're living in the country even though you're close to the city (I went trick-or-treating with their kids, and I had to force myself to not brag that my hauls when I was their age were twice as big as theirs because I got to visit twice as many houses in the same amount of time :), and the street layout is twisty nonsense where even the major roads only have two lanes.
No thank you.
I'll gladly visit NYC again (and I'm sad my trip was only one week and not two), but I never want to live there. I'm happy living in Dallas, though I'm considering a move to Las Vegas for political reasons. Either way, both of those are polar opposites of the NYC suburbs.
https://goo.gl/maps/DYvaWBSLFcP2 1h15m from Rye train station to Fulton subway station on a Tue morning
https://goo.gl/maps/TdQN5FhWF132 55m from Pelham station to Fulton subway.
So door to door, you're still looking at 70 min to 90 min commute one way, with the added stress of possibly dealing with train delays. I wouldn't be able to do that more than a couple years.
My point is, if you want a door to door commute of sub 45 min, consistently, then you would need to be in Hoboken/Jersey City/Secaucus/Weehawken/etc. That whole Hudson County corridor doesn't offer much in the way of decent gyms (swimming pools, racquetball/squash courts, basketball, etc), and neither does it have any decent hiking. People don't really have yards there either.
If you move out of that circle, you do start getting some amenities, but your commute starts looking like 45 to 60+min, and you have to park your car at the train station or get dropped off, etc. It's all personal preference, but for me, I would want all the benefits of owning a car, or all the benefits of not needing to own a car. Living in NJ and working in NYC seems like compromising on both.