802.11n routers can optionally support a feature called beamforming. Specifically for your needs, you would want one that does implicit beamforming.

This allows the router to use multiple antennas to focus the power of the radio signal directionally towards the wireless client (your neighboors computer or other device). Implicit means the wireless client is passive in this setup, the router works alone to support it.

802.11ac equipment has beamforming as part of the base spec instead of being optional. However it is an explicit setup requiring both the router and devices to work together for beamforming. There may be a 802.11ac class router that does the implicit 802.11n style beamforming too, though I've not researched consumer routers in a while.

There's no guarantee that beamforming would alleviate the concrete issues, it would at least let the router direct about a 3db signal increase though.

Mostly an alternative suggestion to the other discussions already going in the other threads. For my own use at home, 802.11ac beamforming is helping my desktop get a nearly solid 700mbit wireless link to my NAS without an ethernet cable. Without beamforming, it was getting around ~500mbit or so and a slightly weaker signal.