Don't go too heavy on the German school of peaceful board gaming. A Board gamer that has fallen to the dark side of non violent optimization game is very hard to get back to the light side of conflict themed games :
I'd suggest (games with a star were GF approved, so they might work in a family setting):
- Nexus Ops (one of the most focused dudes on a map game)
* Summoner Wars (excellent 1v1 tactical game with a strong focus on hand management)
* Chaos in the Old World (it sucks with 3 players. Don't do this! Very good with 4+ , though)
- Descent v2 for Dungeon crawling (many players seem to highly consider Level 7-Omega Protocol, but I have not tried it myself).
* BattleStar Galactica : My prefered coop game by a large margin. Loyalists vs traitors done right. It plays better with 5 IMO
* Android : Netrunner (very good 2 players LCG)
- Game of Thrones (the problem I have with this one is that all games look the same after the 20th. That said, it's still a solid number of playthroughs!)
- Eclipse? (this one is an hybrid between a German and Ameritrash game. I found it cool at first, but I find it somewhat lacks subtlety).
My prefered ones are Starcraft (out of print, and FFG does not hold the licence anymore) and Descent V1 + Road To Legend + about 30 pages of houserules (but Descent v2 is a good substitute). They are both out of print, which is very sad for Starcraft