I live in a 2-storey house and have a wifi router on each floor.  Does having the router in the same room as the device (e.g. internet TV, laptop) make a difference to the connection?  Should the router be placed right next to the device for the optimum result?

Yes and yes, but a decent wifi router should cover the whole house.

5 hours ago, Hamus Yaigh said:

Yes and yes, but a decent wifi router should cover the whole house.

The older and slower 2.4 GHz WiFi band is better at passing through most materials.  The newer and faster 5GHz is much less tolerant of brick/concrete walls so that signal may not cover a whole house very well.

Up to a certain distance there it doesn't matter.

If the distance if too far then the WLAN won't work at all.

And if you are a little below the "won't work at all" distance then it will work slower.

 

For some applications it doesn't matter, like if you look at news or check your email.

For things like watching video in 4k it does matter. 

A dual band wi-fi extender could help if you did not have a router in all floors..

But the 2.4/5 router I got from 3BB covers my large house and garden no problem. Of course the signal will deteriorate the further you move from the router.

Of course it does, depending on the wall material and distance. At the extreme end a Faraday cage configuration will block all WiFi on the other, location of router  could also impact signal. At my US home (Wood frame three floors,) I had to have a repeater, near the stairs where the signal was the strongest , and it repeated the signal to the rest of the floor. I think the name of the device was called TP LINK.  If you are having problems try moving your router higher or as much as you can to see if it improves your situation. I don't know much about these things, I just did what I was advised and it worked for me, , There are also other devices that will expand your range but I cant remember what they were, Perhaps someone more knowledgeable than my will comment on that, or google it.