Hello @Kstein
WiFi client devices (your TV in this case) decide which access point to connect to. There are a number of different possible reasons your TV may be choosing to connect to a more distant access point, though.
Which of those three is the one that is connected directly to your internet service? If it's the Playroom unit, then you may be able to get the TV to connect to the closer access point by simply unplugging the TV from the wall (not just turning it "off", but completely removing power) for a minute or two, then plugging it back in. Once it powers up, then check to see which access point it connected to.
Another potential explanation could be interference. Do you have a sound bar that supports wireless subwoofer / surround speakers near that TV? Or could the TV have such a feature built in? Those devices typically use the same part of the 5GHz frequencies used by Nest WiFi, which can impact both the mesh interconnect (the links the points use to talk to each other) and WiFi client device connections in the 5GHz band. If you do have something like that, you might try unplugging it, then unplug the TV (as described in the paragraph above) to see if it makes a difference. If you do have something like a soundbar causing problems, solving that gets more complicated. But, I would try these steps before moving on to potential solutions.
