Great game for new 360 owners!
Saints Row has a wide variety of missions and mini games to keep you busy. The world/city the game takes place in is huge. There are a large number of great vehicles to steal and drive. The characters and their respective voice acting is very well done. And the ability to customize your character in this game is really cool. Making each main character for each game owner likely to be different from the next.
If your looking for a cool Platinum Hits game to check out. I would highly recommend picking up Saints Row for your Xbox 360.