I live in Arlandria/the very north part of Del Ray on the Arlington-Alexandria border. I'm a mom of a toddler and love to bike. I live right off the Four Mile Run Trail. Super walkable and bikeable here with a lot of small businesses with local character. My house was a fixer-upper townhouse for <500k (we renovated) with a front and back yard. Finished/turnkey homes in the neighborhood can go for 500-700k, though they are small.
I will say, I'm not as picky about schools as many DC folks, and Alexandria's schools are known to be less than top-notch (among the very elite schools in the area). So I take "bad" with a grain of salt. I grew up in truly bad schools.
As for diversity, I think it's starting to gentrify a bit, but still a lot of diversity here. I'm medium-skinned Italian-American but pass for Latina and often get spoken to in Spanish here

Lots of Salvadorian and Black longtime residents. The further south you go from the Four Mile Run stream into actual Del Ray, it gets whiter.
Only downside is there's no metro within 1mi, though that will change when the Potomac Yard metro is finished (supposedly soon).
I like a lot of the same characteristics that you do, OP, and I don't have a car. I think this is the perfect location for urban living but peaceful, family-friendly living.