My suggestions

If you want Xbox 360 games for easy acheivements, these are games that I would suggest:

Destroy All Humans! Path of the Furon
Halo 3: ODST

If you want games to just enjoy and have fun, either with online or just the campaign...or campaigns, these are games that I would suggest:

GTA IV
Call of Duty 4: Modern Warfare
Call of Duty: Modern Warfare 2
Call of Duty 5: World at War
Halo 3
Earth Defense Force 2017 (Voted one of the most sould crushing achievment games of all time)
Battlefield: Bad Company
Castle Crashers (arcade game)

I will update this post whenever I get an idea of another game. If you have suggestions of games, post it as a comment.