In the late 80s/early 90s, my parents wouldn't let us have a game console, but somehow trying to bed hookers in Leisure Suit Larry was okay for their pre-teen. IDK.
If it's the humor that made LSL good for you, the Space Quest series is an easy leap. Or Freddy Pharkas. Plus lots of Lucasarts games like Monkey Island, Indiana Jones, Maniac Mansion...
The Police Quest series is my favorite. PQ1 is easily in my top games of all time. Followed very closely by the first Gabriel Knight game. I went to New Orleans years back for work and the best thing I got to do was look out over Lafayette Park and St Louis Cathedral from the same vantage point as in the game. Maybe silly, but it was a really fulfilling moment.
Oh, I always really liked the Quest for Glory games too, though I don't think I ever finished any of them. Maybe I should work on that this year.