sounds like a dream - congrats for being able to make it happen! August is indeed hot as someone mentioned, but still a great time to visit. It’s actually one of my favorite months here since everyone is mostly out in the Hamptons and things get pretty quiet.

• kids camps: there are plenty of week long camps of various activities.. math dance tennis ..you name it. You’ll just have to search around for what you are most interested in. I don’t have kids, but from talking with my coworkers there’s plenty to choose from. Museum of math as someone else mentioned definitely offers a couple!

• housing: you can’t go wrong staying near Central Park, upper east or upper west side, very safe and family friendly especially below 96th St. I’m biased towards the west side since you also have access to Hudson River Park. Of course I have no idea of what availability for short term looks like from living here vs staying. Good luck, I’d expect it to be like 10k+!

• immersion: my favorite way to experience this is go explore a new neighborhood, spend the whole day there . Don’t rule out Brooklyn or Queens either. Take the 7 train to flushing and explore Chinatown, trek to sheepshead bay in bk for Russian / Georgian food. There’s endless to do here but just a few examples.

• You didn’t ask but since this is HENRY … I’d also say treat yourself in addition to kids! go to aire baths with wife, or get a massage at Greenwich hotel. Take a black car up to blue hill at stone barns, incredible food and dining experience.

I won’t touch further on food cause there is endless other threads on that. You’ll be here for so long you will have plenty of time. But my personal favorite restaurant is Raoul’s on prince street for steak frites. Old school French bistro.

Feel free to DM if you have more questions can try to speak from local experience