You might like:

The Talos Principle — Basically Portal but... different. Physics, timing, & world-affecting-zappy-device puzzles. No actual portals but it's pretty similar. A "there's more going on" story. Quite good.

The Witness — Myst-like I guess? In that you're exploring an island and solving puzzles and piecing together a story, kinda. But the puzzles are all variations on one sort. Elements get added, things get weird, lateral thinking becomes necessary. It's good.

The Talos Principle really had me thinking about it when not playing. I halfway thought I was going to hear a voice when I got on the elevator at work.

Puzzle games, especially good ones, are relatively rare, that's the problem. They're one shot, easy to spoil... And then there is a risk that the puzzle will turn out too hard.

Thank you for the suggestions. I'll check out both of those.

Edit: Just bought Talos for the PS4! Once again, thanks! When I'm done with it, I'll check out Witness.

I'll second The Witness as a great game. Very different, and beautifully designed.

Stephen's Sausage Roll is great little puzzle game I've spent hours playing. Not an easy game by any means, but it's easy to get lost in it & kill a few hours. The puzzles have no time component, which is great, I'm not a fast thinker so timers just annoy me.

There was Portal 2, which was pretty fun.