Can you recommend any titles for XBOX360 that aren't hardcore?

[EaglesEye379]

If you mean easy to pick up and play but has depth then I recommend these to start:

Viva Pinata: Trouble in Paradise
Kameo

Eternal Sonata/Tales of Vesperia/Lost Odyssey - they can get hard later in the game.

I know you said disc-based but you cant go wrong with Braid as well!