I'm a Brit who has been living in NYC for the past 15 months.
The ways the Newspapers bang on out about it you'd imagine it is some kind of anarchic hell hole right now! It's not - NYC is still here, and it's a great city, and so long as you're careful and sensible you'll likely be fine (for example, watching for pickpockets, don't ride the subway alone at 3am etc.) I've also spent many years living in London, Hong Kong and Tokyo and don't feel that much more unsafe here than I did in London, and I live in a part of Brooklyn traditionally considered "the hood". Areas like Times Square and midtown can be a wee bit dodgy, and there is a big problem with homelessness and mental illness, especially on the subway, but for the most part if you mind your own business people won't bother you.
There is a lot to do here, it is great fun, and I think your sons would love it here. And it doesn't need to be stressful - perfectly possible to have a relaxing time here - leisurely brunch and people watching, stroll in the park, even enjoy a Korean spa etc.
One thing I will say is that it is significantly more expensive than London or Tokyo (my supermarket spending is 3x what it was in London) and eating out, too - especially when you factor in the essentially obligatory 20% tip.
After the pandemic and now what is happening with Ukraine, I have personally resolved to grab chances when they come along because you never know when you might NOT be able to travel or whatever for another year or two.
Good luck OP, hope you can destress soon!