I’m sorry, but so few of these urban environments are affordable with good schools. I lived in Philadelphia and we chose to leave when our son was young because the schools generally aren’t good (most don’t even have libraries, but this is a whole different topic), the green space barely exists and isn’t maintained, and I’d never feel safe with my kid taking the transit.
NYC and Boston seem like the only east coast options and those are very expensive. What other options are there on the East Coast?
Philadelphia is absolutely an option, but it depends on the neighborhood. Eg if you live in the penn alexander, greenfield, or meredith catchments you have a great elementary/middle school and there are lot of kids of late elementary/early middle school age moving around the city independently.
I live in west philly and it is great: the park is excellent and lots of kids safely go there by themselves, the local school is very good. Transit (specifically the trolley) is good and safe.