[GaryProtein]

The entry door is the biggest concern.

When I was in my residency in Boston, I lived in a high rise. The MOST important improvement to keep sound out of the hallway was to place a quality gasket all the way around the entry door frame to the apartment. That included adding an oak saddle to the OUTSIDE of the door for it to close against. The saddle can be screwed or eppoxied to the floor so the gasket could go around the floor part of the door frame also. You should have to lean on or slam the door closed to get compression of the gasket for the door to latch closed to stop sound permeation through the door.

There is little you can do to prevent sound from traveling through walls. A carpet will help stop some sound going through the floor. The ceiling has almost nothing you can do to stop sound penetration.