Castle Panic (this has been a favorite for years, it is cooperative with a bunch of “rules” for each card, I get confused but my kids really like it and my youngest long before he could read started playing with us and learning strategy and he is the one that really likes it.)
Arrethtrae (this game is by Chuch Black who wrote the Kingdom Series, another cooperative game with strategy that we really enjoy playing).
We rarely pay attention to the suggested ages, and just learn together, even when my kids were quite young they enjoyed challenging games because we played them together. GeekDad has a huge review page of board games. When I am looking for new ones I often check there.