I was answering this question recently for a friend of mine, only substitute "wife" for "neighbors." He was interested in taking up the electric guitar while at the same time remaining married.
The answer I came up with for him, specifically was a DigiTech RP255.
It is a multi-purpose item with all of this functionality in a single unit:
- Amp / Cabinet modeler
- Effects modeler
- Expression pedal (for wah, volume pedal, other controls, etc.)
- USB recording interface
- Drum machine
- 20-second looper
Before I recommended it to him, I went to my local GC and played one through some headphones. I thought it sounded pretty good - and certainly outgunned my Pocket Pod for pure functionality. Is this (or something like it) the be all and and all of tone? Of course not. But this (or something like it) can provide all sorts of options for practicing while leaving your neighbor (or spouse!) in peace.