Intermittently high ping times to router via Wi-Fi
Clearly you have an interference problem. Interference can come from passive elements like aluminum wall studs or thick floors, but those are not likely to show the periodic pattern you see. So something electric or electronic is periodically emitting. Finding it may be expensive or tough, but you have a few options.
Graph more. It would be nice to make sure that this isn't a bandwidth limitation of your own creation. Looking at the bandwidth consumed on your uplink and each of the clients might lead to a similar looking graph and the source of your problem.
Upgrade firmware. Being on the latest firmware could get you past a bug in their code causing this. Plus it helps reduce the chances of your router being remotely compromised.
Mitigate it. Get a wifi analyzer for your phone. Look at who is using what bands when purple is pokey particularly. You may find that switching from 7 to 1 or 14 takes care of your problem. The analyzer should show you how the channels spread out into each other, so if you are in a really busy area going for the in-betweens of 4 or 11 would let you reduce the congestion.
Migrate. Can you move the WAP to a different location? Placing it in a place just a foot away can significantly effect propagation within a building.
Ground it. Make sure all of your AV equipment (TV's, stereos, etc.) is properly grounded.
Find it. You could use a spectrum analyzer and a directional antenna to find the emitter, but the spectrum analyzer is big bucks. If you know a HAM radio operator they may have this gear laying around already; offer them food and don't be surprised if more than one shows up. The HAM will also know the FCC regs inside and out which will be great if you actually find the source. Without bribing anyone you could try cutting things off and see if gets better, but it might not be your stuff causing the problem. When dealing with VCR's and TV's you may need to completely unplug them.
I had it with an idle Wi-Fi network (Windows 7, various TP-LINK USB adapters). The ping fluctuates, making any remote terminal work a nightmare.
Solved by putting a constant load on the Wi-Fi network (e.g. fetching a small file from the router's web server in a loop).
To me, the intermittent nature indicates a hardware problem. Wireless routers go bad often. I'd try a new router and see if that doesn't resolve it. Maybe you can replace under warranty with Netgear if it's not too old?
Or you could always run a bunch of cat-5 and mini switches everywhere, the wired part of the router is probably fine.