My kids are in a school where more than half the kids are non-white and around half the kids have low socioeconomic status (SES) based on free/reduced-price lunch numbers despite our district being high-SES compared to other districts in our state. We have a good base of racial diversity although that diversity is mostly Hispanic (dual-language school).
A teacher at our elementary school once said that socializing across SES normally happens only if parents make a point of providing opportunities for that to happen with the kids. Kids have lots of birthday parties at local parks - I've attended several of these gatherings where the kind-hearted bilingual parents switched over to English so that I could be a part of the conversation - while my kids are bilingual, I am a typical American and only speak English.
As both a parent of participants and as a coach in youth sports, I'll say the rec leagues sometimes provide good opportunities for that mixing of different SES kids. It often falls apart though - we have youth sports leagues where the participation and lost opportunity costs due to heavy practice/travel time seem to screen out low-SES kids.
It's kind of funny, but my family basically lives in small-town America but has wound up in a better school district in our state that also has some racial and SES diversity in the population. It's working as both a good school district and opportunity for kids of different SES and race to grow up together. Longer term, problems with affordable housing are probably going to blow some of these opportunities away.
I can't say I noticed any difference in the schools. Mclean had great test scores, but that's because it has managed to zone out almost all the middle and lower-income people and the working class immigrants. My wife and I have been struggling with where to send our daughter to school. I don't think it's worth it pay a big premium to buy in the higher-ranked school districts. Unless the district has an actual gang problem, it's generic "McEducation" almost everywhere. If our daughter shows tendencies of being a creative thinker we'll likely do private for at least high school. If she shows a high tolerance for petty tyranny we'll likely do public somewhere in Anne Arundel (which is close to DC but far enough away where she might meet some blue collar people).
What they don't get is good college counseling, which I'm learning to my dismay with the boy getting ready to apply, so maybe a good rationalist/cost-saving approach here is to send your kid to public high school but hire a college counselor. (No idea if that's a thing you can do).