Consider getting a pair of Auralex Gramma isolation platforms to put your speakers on. They will isolate the speaker from the floor and keep the bass from bleeding into the next apartment while allowing the speaker to project into your room. You would still need to be sensible about volume levels as well. They are about $50 each and work well. It is a minimal investment to keep the peace. The headphone idea also makes a lot of sense.
Apartment Drama
Hi- I recently moved from my house to a 2nd floor apt with 1 apt on each side and 1 below. 3pm today I turned my stereo on for the 1st time. Low volume IMO. Hard to describe but no problem having a conversation without even raising my voice. within 10 minutes my neighbor knocked on my door acting irratated demanding I turn the volume down. WTF? Now what. Do I have any rights or do I have to obey this jerk?