How to find a router at an unknown location in a house?
You are going to laugh, but I was in the same situation. I could not find my mother-in-law's router as the cable company had installed it.
When my nephews came over they wanted to use WIFI on their Samsung Tablet. I told them that the WIFI code is on a sticker at the bottom of the router. They turned the whole house upside down, and found the router on a top shelf in the cupboard. I have no idea why it was placed there, maybe for reception. The wire running to it went through a wall, so it was obviously not an easy place to install. That technician really gave it his best.
So find some kids with a tablet and invite them over. They'll find the router if that is what stands between them and Facebook.
If you have a Android smartphone or tablet, you can use the WiFi Analyzer app. It has a screen dedicated to detecting proximity of access points:
Walk around the house and see where the signal is the strongest.
Barring an obvious wire leading to it, then searching by WiFi signal strength should be good too. But not the "walk around blindly with a strength meter" approach, use an app that will map it for you.
ekahau Heat Mapper
It can make a map for you, that should give you a better idea of which corners to be concentrating your search in. It's for Windows, How-To Geek has a little guide about it. They say it's "essentially the free version of the multi-thousand-dollar Ekahau SiteSurvey."
The best part: It may find the router for you.
once we finished walking the entire map, HeatMapper pinpointed the location of the two access points within our office with uncanny precision. Look at the red arrows on the map below:
There are some Android/iPhone apps that should be similar too, try searching for one that works on your device. Maybe Telstra Wi-Fi Maximiser (for Android), here's it's screenshot:
My first ideas were to:
I'd just follow the house wiring, starting from where they enter the house, and checking wherever the main cable or telephone "junctions" are, you didn't say if it's telephone/dsl, or tv (coax) cable, or pure network cable or fiber optic, but they all enter the house from somewhere. Unless you've got all underground utilities... but they probably don't enter through the basement, or "tube" would still come up from the ground somewhere outside the house.
If some technician installed the router / network cable recently (they weren't built into the house originally) then try looking around the "main" tv or telephone areas, high & low anywhere within reach, check for mystery power cords plugged in around there and follow them.
Phone the internet provider and ask them where they installed it. Maybe most of the houses in the area have a "standard" layout, or their installers always put them on the floor under tv's, or in the attics or someplace unexpected. Or they may have been good enough to take note of where it is in that house.