You're after a point and click/ graphic adventure title, then.
Grim Fandango has recently been re-released with a few modern tweaks. Possibly the best in the genre, was the last AAA graphic adventure game.
Daedalic, a German studio, make modern point and clicks. I've played Edna & Harvey: Harvey's New Eyes, and it was a lot of fun. They also made the Deponia series, which is well regarded.
The Monkey Island games are great. Not sure if they're available for modern systems.
Broken Age is a new game from Tim Schafer's studio, Double Fine (Tim Schafer being the lead on the Monkey Island, Grim Fandango, and other Lucas Arts adventure games). Part one is available, part 2 is due in the next few months.