You probably won't ever make the neighbors happy.I have my own home and the neighbors hear my music 30 yards away in their homes.I just turn it down a bit when I know they are getting ready for beddy by.I listen to the bass heavy rock during the day and early eve then spin the mellow stuff later t night.You have to be careful no one calls the cops because then you will always worry even more.It hasn't happened to me YET! Try some large pieces of carpet padding on the wall.Maybe 4x6 then find some nice looking tapestry or rugs to cover the padding.Or get head phones to use at night or other times the neighbors are home.
Budget Insulation Advice
I live in an apartment with relatively thin walls. The only way to avoid neighborly complaints is to play music at a level where my receiver isn't as detailed as I want to hear. Basically I want to know if there's any cheap (read not specifically designed for this purpose) way of insulating the wall. The wall is probably around 125 sq ft and I really don't want to spend more than $200 for the project. Looks aren't important and I don't need to sound-proof just reduce the amount of sound that passes through the wall. Also would you have any recommendations for compensating for the newly 'deadened' room.