I really like those bite-sized escape-the-room puzzles where the game dumps your inventory (or sometimes not) and traps you in a scene.  You have to find all the interactive objects and figure out how to use them to escape.  My favorite example is when Guybrush is arrested in MI2.  There's also the pit of acid scene, and the scene in SoMI where you're under water.  And of course the cannibal hut.  It's a nice break from the game.  When you're on the Sea Monkey trying to find Monkey Island, the scope of the puzzles is a bit larger than being stuck in a room, but it still had that feel.

As for non-linear, finding the map pieces in MI2 has to be the best puzzle design I've ever seen in a game.  That entire game is amazing.  There's so much to explore and do.  I actually miss getting stumped.  It took me a month to figure out some of those puzzles.  I completed both stories in Broken Age in an afternoon.

Something you don't see a lot but I always appreciated is when things come full circle and you arrive back where the story began.  When Guybrush makes it back to Melee island with his root beer potion, he absolutely dominates everyone in his path.  You feel like he's finally become a pirate and his arc is complete.  And he gets the girl in the end.

And as a game developer, you can reuse a location of the game.  A necessity when disk space and budgets are/were limited.