Generally no permission is required in Public ,
however if you want to close off a section of public footpath or road you need to plan it and go down to the City hall on a tuesday afternoon at 1pm and talk to the roads dept about getting a licence for that. It might be worthwhile even just letting them know you’ll be shooting if you’re going to have a big group blocking up the boardwalk , but if you’re not going to get in the way , then you don’t need to.
As for public walking by , as long as only actors are in focus and identifiable then it’s OK but if any members of the public are Identifiably in shot , get a written release from them.
Business premises you’ll need to get written clearance if they are identifiable
Most are cool with it , give em a thanks in the credits