The sum total of this letter to Lucilius is found in this quote:
what benefit is a quiet neighbourhood, if our emotions are in an uproar?
By the time you get to the end of the letter, you see the full picture. Seneca purposely moved to and lived in a raucous part of the city to test himself to see if his mind could be at peace amid all the noise. He wanted to know if he could tune out the noise and still be able to maintain his equanimity.
You may therefore be sure that you are at peace with yourself, when no noise reaches you, when no word shakes you out of yourself, whether it be of flattery or of threat, or merely an empty sound buzzing about you with unmeaning din. "What then?" you say, "is it not sometimes a simpler matter just to avoid the uproar?" I admit this. Accordingly, I shall change from my present quarters. I merely wished to test myself and to give myself practice.
The rest of the letter is a list of things that cause him and others distraction. The noises of the street to other peoples' words; from constant to intermittent noises. If he can master keeping a tranquil mind with all the external noises, he can more fully comprehend how to quiet the disturbances within.
I force my mind to concentrate, and keep it from straying to things outside itself; all outdoors may be bedlam, provided that there is no disturbance within, provided that fear is not wrangling with desire in my breast, provided that meanness and lavishness are not at odds, one harassing the other.
And if all the noises have been managed and you are left with a dead-quiet home and life and yet you are still disturbed, then you have need of further work.
For even when we seek slumber, our sleepless moments are as harassing as the daytime. Real tranquillity is the state reached by an unperverted mind when it is relaxed ... You need not suppose that the soul is at peace when the body is still. Sometimes quiet means disquiet.
One potential solution to address disquietude is to keep our minds busy with good interests. As Proverbs 16:7 mentions, idle hands (and mind) are a devil's workshop.
We must therefore rouse ourselves to action and busy ourselves with interests that are good, as often as we are in the grasp of an uncontrollable sluggishness. Great generals, when they see that their men are mutinous, check them by some sort of labour or keep them busy with small forays. The much occupied man has no time for wantonness, and it is an obvious commonplace that the evils of leisure can be shaken off by hard work.
In sum, stay busy with good interests; don't let the external raucous disturb you with the goal of having a tranquil mind whether in loud or quiet settings.