Moving to Westchester, talk to me about Scarsdale (as compared to river towns)

tl;dr — I want to give my kids the best education I can, but don't want them to turn into entitled jerks. I also want to optimize for commute time and walkability.

Hi there,

I'm moving to Westchester from Brooklyn¹ with my two young kids (oldest starts K in Sept '22). Looking for an urban-ish vibe, good schools and short commutes into the city. Ideally in a more down-to-earth community with somewhat flat terrain. Though unfortunately, I think those last two might be mutually exclusive, which is the crux of my question.

There is a lot to like about Scarsdale — great commute to the city, flat enough that walking around is comfortable and kids can ride bikes and of course amazing schools. I also think I could afford a decent house in the more "affordable" sections of Scarsdale with a budget up to $1M or a little more. And in these "affordable" sections I think I could find people like me / my kids would go to an elementary school with kids they can relate to. But I'm worried about what they will encounter in middle and high school.

I grew up fairly poor / lower middle class in the midwest. And while I've obviously had some career success if I'm considering Scarsdale, I'm never going to fit in with the "summering in the Hamptons" crowd. I don't want my kids to feel immense pressure for conspicuous consumption behavior like expensive European vacations or designer bags or whatever. On the other hand, I think the academic environment could be still good for them. I know it's often referred to as a "pressure cooker", but parenting has to be an aspect of that. I don't care if they go to an Ivy (honestly, I'd prefer MIT/Stanford over Yale/Penn but I digress), but I want them to have the opportunity to achieve academically to the extent they're able and desire to. Basically I want to give them the best education I can while minimizing the risk that my kids turn into entitled douches or resent being the "poor" kids in school.

How accurate are my assumptions / interpretations? Would I be better off sticking to the river towns (Hastings/Dobbs), even if that means that walking / biking around the neighborhood (or to the train station) is much more difficult? Are they actually materially more chill or insulated from extravagant wealth than Scarsdale?

Thanks in advance, sorry for another "moving to Westchester" post.

^1. Okay, technically I'm moving from Austin. When leaving Brooklyn it was a choice between moving to Westchester or trying Austin. We tried Austin for a couple years and it wasn't for us, so we're going with ole Bestchester. Which makes it harder to just visit these towns and answer my own questions.