Room treatment ideas for annoying external noises

Another option -- just turn up the volume!

Improve the sound of your audio system.

When the audio sound is unnatural, human ears must adjust to that unnatural sound to hear clearly. Dog barking and construction sound are natural sound and they disrupt listener's concentration to unnatural sounds (audio sound) because human ears react to natural sound much easier.

If audio sound is truly natural, human ears don't need to do (adjust) anything for the audio sound. And there will be no listener's fatigue.

Alex/Wavetouch

What you are looking for is how to soundproof a room, not treat it. There is tons of information on Google and YouTube for you to see what is in your budget.

When the sound of audio is closer to natural sound, other natural sounds will not bother listening as much. Rather the listener might enjoy the audio sound and other natural sounds together like the listener is in a live music cafe. 

Alex/Wavetouch

@mihorn 

That is true, but the SPL would still be higher/sub-optimal. Playing over loud noise just means louder. Not better.

@ghdprentice 

Well the sound-proofing doesn't need to be expensive. Upgrading can happen along the way.