>pretty Jewish neighborhoods

The commute to southie will probably involve a hop from the Green Line to the Red Line, but Brighton would probably be a good choice for this requirement. I lived in multiple apartments in Brighton ranging from close to Cleveland Circle, Brighton Center, and Oak Sq. I constantly had Jewish neighbors and it was very normal to see families walking around in full garb.

Depending on how many roommates you want, your budget should be fine in Brighton (depending on quality of apartment). Before I moved away, I shared a 2bd 1 bath apartment with my wife for only $1800 in 2018. The place was problematic, but we wanted a cheap place so we could save for a home.

Brighton is also filled with people your age. It's quieter than Allston, but close enough to enjoy what Allston offers without the crazy college kid antics.