I also live in a neighborhood and I do the vast majority of my practicing at the range because there are kids around. During the archery season I do occasionally shoot 20 yards into my garage, to make sure I haven't knocked something loose, only during the school day. I used to use hay bales for a backstop but they are tough on the vanes. Try hanging a couple of layers of carpet over a 2x4. That should stop a miss without tearing up the arrows. Besides you can probably get carpet waste for free from any carpet place. They have to pay to dispose of it.

HH