Try a evil twin attack and social engineer them into giving you it. Or you can check if WPS is enabled or not to crack the 8-digit pin the router, which will usually take you 8 hours or so since its only 8-digits you are cracking. Cracking with a dictionary almost always fail.
And, exactly why are you fucking with your neighbors? After your in, you are going to run Armitage and exploit their computers? I don't see the point. I guess you are just testing what you are learning on someone you don't have permission to do it on, and for the "lulz" of course.
I've never tried an evil twin before, so I'll do some research and whatnot but would I have to go any further than replicating their AP and one way or another bumping them off theirs, make them jump to mine and in doing so force them to re-enter the password that I'd just then have?
And to answer your question: I really am doing it do see if I can gain access to their network. I don't plan on stealing anything or spying, my goal is to just get into the network, and then try to use hydra to hop on the router if I can. Nothing malicious in mind.
Also thanks to everyone with the brute-force suggestions, I'm new here and I appreciate the time taken to respond a TON!
I'll probably try some different brute-force ideas before I go evil twin, the less invasive I can be, the better while I do this.
PS the router is NOT WPS enabled so I can't use any of those suggestions :/