One sound-permeable entry point that you can fix with relative ease: replacing your hollow core interior doors.
Interior doors comprise a far larger expanse of shared-wall than you might think at first. If the wall you share with the noisy area is 80 square feet (i.e., the typical 8 feet tall, and then another 10 feet wide), then the door represents close to 20% of that area.
What Is The Weak Point?
Interior walls have two sheet of drywall, one on each side, and the sound-insulating space between those sheets. Not great sound-proofing, but not the worst, either. The weak point: that hollow-core door of yours.
Hollow-core doors have just two advantages. They are relatively inexpensive, and they are easy to swing.
But they also punch through at the slightest impact. They feel and look cheap, and I don't mean inexpensive.
When it comes to sound-proofing, one of the most recommended practices by residential sound-proofing experts: Replace your hollow core doors with solid doors.
How To Do It
As long as you stick to the same dimensions, it is strictly a one-for-one replacement process. Screw and hinge placement should be the same, though not necessarily.
Make sure that the hinges match up the same and that the screws need to either match up, too, or be far enough away from existing holes so that you can drill new, strong holes.
If the new holes are close enough to the old holes that they merge, then installation will be far more difficult.
There is redundancy in hinge screw placement, so you could--if you had to--sacrifice a screw. But because you are dealing with the increased weight of a solid wood door, every screw counts.
You will absolutely notice the difference in noise between a hollow core door and a solid wood door in terms of reducing sound transmission.