I just recently bought a PS4 and would like to be able to play it in my living & bedroom without moving the console back and forth so PS TV would be the perfect solution.

I remember them getting down to like $40 shortly after releasing but I had no need for one back then and now none of my local retailers carry them and I can't find them anywhere online for under $100.

Does anybody know where I can find one for cheap?

Get an i5 based device and use that. There's a reason Sony discontinued the Vita TV and, believe it or not, isn't because it sold terribly. There's input lag when playing PS4 games (Which isn't in the handheld Vita) on the thing and it makes remote play unusable.

What is this i5 device you speak of?

It's a processor.  Remote play on PC requires an I5 or greater get a laptop, or small PC.  Use this if you don't want to wire your controller:

https://www.playstation.com/en-us/explore/accessories/gaming-controllers/dualshock-4-usb-wireless-adaptor/