That pogoplug thing looks nasty, no thanks.
So let me get this right.. A box that allows you to share up to 2xusb3, 1xusb2, SD card, usm/sata. with a gig interface. Along with automatic backup of your computers files, streaming your video and music for $20 is "nasty" What you don't like the color of its logo?
If you want you can put debian or arch linux on it and do whatever you want with it, etc. etc..
To the OP -- with your budget, I know for sure you could do this. Get the $20 pogo, setup plex - get 2x35$ chromecasts to connect to your TVs - or just one you move about, so your under 100$ here and there you go your rocking.. You can watch video on your TV's you can access your files from any device on your network, etc. etc.
I have a older pogo, but the series 4 will be here soon and I have a chrome to play with so pretty sure I could help you through any setup. But I also read that vizio added plex to their apps.
"January 7, 2014 — VIZIO, America’s #1 smart TV company1, announced today the addition of more popular apps, Ultra HD streaming and second screen experiences to their popular VIZIO Internet Apps Plus™ platform. VIZIO Internet Apps sales are sure to continue to grow with new apps including Spotify, Lyve, AirCastLive, Baeble Music and Plex."
So quite possible you could stream directly to your TV without the need of chromecast. This puts you other than some setup time at $20... But then again its "nasty"
And also other nasty feature it has - is you can share files over the internet.. So say you wanted to watch a movie while your away from home, or needed access files, etc.. You just point your browser to the pogo page and log in and there are your files be it on your local, or in your free cloud storage you get with your account, etc.
Worse case - what your out the cost of stop after work for a couple beers Or sure go spend $$ -- here you go.. This one is $150 - under budget.
This is entry level nas - has same usb3 and usb2 ports an esata - with 2 bays. So you could take your external drives out and put them in. Not sure if it has support ntfs, hfs+, ext2, and all the formats that the pogo supports but this is pretty much the same thing for just more money and bigger box, etc. Since you never mentioned you needed actual drive bays, etc..
If that doesn't work your out $$, if the pogo doesn't work your out pennies and could just destroy it with a hammer taking out your frustration and your out really the cost of a couple of beers with the boys..