Forget messing with the position of your subwoofer. It shouldn't help much, if any at all. In fact, I've had more than one experience where positioning a subwoofer in a corner on a wall of an adjacent room yielded less bass in that adjacent room than when it was farther away from it, which is definitely understandable.
And, IMO, don't waste your time with attempting to control this problem passively (adding mass to your walls, etc). I made this mistake in my last apartment. Didn't do me a damn bit of good. Only a major hassle when it was time to leave. And after all the time I spent redoing things before I left, I was still charged fees for it.
If you, like many people (myself included), refuse to resort to headphones (they have plenty of their own compromises, as does everything), then my suggestion is this..
1. Dipole loudspeakers. If at all possible, re-arrange your room so that the location of the main problem areas are more to the sides, top, or bottom of the speakers. As with most dipoles, you don't want them too close to a wall, and in this case, I think it'd help even more to have them farther away from any walls or large flat surfaces (except for maybe the floor, of course). If re-arranging your room isn't possible, this might all be hopeless, as I don't think dipoles will help a great deal if the annoyed neighbors are directly on the other side of the wall right behind them. If it's one main wall that's being shared, the speakers need to be perpendicular to it.
2. If you're used to your brain being rattled with sub 40 Hz bass notes, forget all about it and pretend it doesn't exist. Get yourself a ButtKicker LFE or two. I have a pair, but they're still collecting dust since I need a new couch anyway. Expect usable bass extension to 35-40 Hz at the very most and leave it at that.
3. A simple pic of your room would be great. If it's just one photo, either take it from the listening position, or try to get the entire room in the photo. If you feel funny doing that, put it on a free image hosting server for the time being, then remove it whenever you want once this thread has settled down.
4. People will offer you their thoughts/recommendations/opinions in regards to what you should do, how you should do it, and what things you should get to do it that way.
5. Do what was decided during step #4, and keep going until it's completed, taking interesting photos every now and then throughout the process so we can all come here and stare at them when we're bored.
6. If all goes well, you end up very satisfied with everything you've done and it works out ok with your neighbors at very reasonable listening levels.
7. You take even more pics of your completed work so we can all stare at it and tell you how good you did, etc.
