Commoner

The Xiaomi Redmi Note 3 would make a great gift for someone who's not comfortable with switching to a modern Smartphone like my Mom.

It's priced modestly at $170 USD but you get pretty much flagship specs. It has a MediaTek Helio X10 MT6795 Octocore Processor clocked at 2.2 Gighz, PowerVR G6200 GPU, 3 GB Ram, 32 GB Internal Storage, 5.5 inch 1080p IPS Display, a Fingerprint Scanner, an IR Blaster, and a decent 13 megapixel camera. It's also got a premium feel with it's all metal body and has a 4000 mAh battery that can give the kind of battery life that people with non-smartphones have gotten used to.

But the main reason I'm suggesting this phone as a gift for someone who's not used to Smartphones is that it's MIUI 7 OS has a Lite Mode which is super simple to use, particularly for an older person who doesn't have good eyesight.

To get an idea of what Lite Mode is like so you can judge for yourself, there's a youtube video which explain it here :