Conversion from USB to HDMI isn't directly possible. There are (poorly-named) USB-to-whatever adapters, but they're actually just video cards with a USB interface instead of PCI. Problem is, USB doesn't have the bandwidth for raw video. If you've ever been.. eh.. luck enough to use a laptop with an external monitor connected with a USB interface, you'll quickly realize how painfully slow those things are. Full-screen video at 30fps? Not happening.
Good HDMI cables can go quite a distance, but when you cross the threshold of reliability, they turn sour pretty quickly. When you're at the threshold, problems can be intermittent and thus absolutely no fun to troubleshoot. Success with HDMI-over-UTP extenders varies widely. VGA over UTP will work but may ghost a little.
The media player market is in shambles right now. AppleTV works really well if you're totally invested in the iTunes ecosphere. Many other players (Roku, Chromecast, FireTV) have Plex clients available, but then you get into support issues like getting media onto the server device, and training grandma how to use the client. But, you'll have some of those problems anyway just having media on a PC. If you want to avoid that, pick a box, sign her up for Netflix, Amazon Prime, and/or Hulu Plus, and hope she has a good Internet package.
Basically: This stuff is all a lot harder than it should be. You can thank the MPAA and various content producers / distributors for that. The technology is there. But, the content guys are trying to strong-arm the consumer into doing things their own way, while consumers respond by pirating everything on the Internet. Anyone interested in taking advantage of local online storage of legally-acquired media is pretty much trapped in the cross-fire. Vendors that try to manufacturer hardware to make it possible either get sued, lose (or never gain) the ability to license all the necessary (....well... "prolific" anyway) codecs, find themselves unable to strike deals with distributors, or otherwise die on the vine. Progress is grand.