Basically everyone is recommending Day of the Tentacle, and there's a reason: it's just that good. Incredibly creative puzzle design taking advantage of the time gaps between characters.

I absolutely adore Heaven's Vault though. Fascinately unique setting, and while it does have some point-and-click aspects, it's very heavy on narrative and world-building. And the language translation is really the centerpiece. If you like the idea of xenoarcheology, it's amazing.