Your question is unclear...
I think you are in a multi-unit building, and seeking to minimize sound transmission into other units. Therefore you seek to create a cocoon near your screens/monitors that contains sound, with a lower level in the rest of the room, and so less transmission to your neightbors.
Am I close?
If so, I'm afraid you aren't going to be happy when you find out what it takes to isolate sound. Here's the master reference.
Chpt. 16 talks about sound isolation, which I'll wager is beyond your scope, while Chpts 12 and 15 may provide some useful options for absorbing sound, but they will also have a direct and audible influence on sound within the room. Bass will be a special problem, as it's hard to absorb and travels very well thorugh structures.
What do you think? Am I close?