[kombookcha]

+1 for Root!

For a nice entry game for a group setting, I recommend Carcassonne. It has a simple and engaging basic gameplay with a surprising amount of depth, that can easily be scaled up and down in complexity depending on your group's preference and experience level by simply adding more pieces/mechanics.

[leethargo]

Carcassonne is also really nice with children. You can start them on just the "puzzle" aspect on attaching matching tiles, without scoring.

Our oldest child is now capable of the base game, and I can still make it interesting for me by going for secondary objectives, such as filling difficult gaps ;-)

[kombookcha]

Very clever to introduce it to kids as purely a puzzle game! I'll keep that in mind.

When my girlfriend and I play, we sometimes give unofficial bonus points as compensation for suboptimal plays that fill out unseemly gaps that would otherwise stay open. Makes for a nice, aesthetic endstate board without handwringing over your score :b