Your back-to-schooler is always on his phone. He loves watching YouTube videos. You love a bargain. Sounds like Chromecast, which allows him to blow up those phone videos to TV size, is the perfect gift.
She is taking your old TV to the dorm, but she's annoyed that she can't watch all her favorite apps on there because her PlayStation 4 doesn't get WWE. The Roku Stick does, along with thousands of other apps.
If your back-to-schooler has a bunch of stuff on iTunes, or he just wants something that looks and feels a lot like his iPhone, the new Apple TV is just the ticket. In addition to numerous TV apps it also works with many of the games and other apps he might already own.
Then again, maybe your student is an Amazon Prime junkie, glomming off your Prime account to binge on TV free shows and movies after recovering from a long school year. Nothing wrong with that, but maybe she needs a streamer of her own?