Chiming in late...

. I second the comment that, should you run a wire, it's really straightforward to add a new connector to it. The tools are designed to be idiot-proof, since electricians are often idiots. This means you may need to test that you terminated the wire correctly. At worst, I've needed 3 attempts to get a wire properly terminated.

. After that, the idea of doing a ceiling-mounted AP, powered with PoE seems pretty slick. That's the "dollar no cost, do it properly" solution.

. If you really want to stick with wireless, the beamforming stuff that people have talked about here is going to be an odd thing. Most APs will have antennae arranged in a circle of some sort, meaning that they can steer horizontally, like a lighthouse, but can't steer vertically. One of the things to play with, then, is tilting the AP, such that it has the chance to beam at a downward angle. This will require a huge amount of experimentation to get right.

. I don't know if it's feasible, but you could also investigate wireline networking. If the two apartments are on separate power meters, this would seem less likely to work, but it's certainly worth a shot.