I wonder how this interacts with the right to peaceably assemble, especially given the often political nature of punk music.

Cities can police nuisances, sure, but they cannot craft statutes abrogating first amendment rights that are not narrowly tailored to the perceived harm.

There were a few laws against public dancing in the late 1800s that got struck down under this sort of reasoning.

I'm not sure what the current state of constitutional limits on nuisance laws are, but the Boston statute does seem very broad.