Congrats on getting your 360! (Wii60 owner here :) )
Well like you said Ninja Gaiden II is coming out in the near future. DMC4 is also pretty good if you haven't tried that out yet.
The obvious game if you're interested in that type of game is GTAIV (I just picked up my copy and I'm enjoying in between finishing playing Lost Odyssey :) )
It's not as good as Lost Odyssey (IMO), but you might want to give Blue Dragon a try. (You may be able to pick it up for cheap, too!)
If you don't have it yet, COD4 is of course a great FPS.
I'm not sure if you've played the older ones(PS2 Katamari Damacy games), but even if you haven't Beautiful Katamari is a really fun game definitely worth checking out.
Oh and you may want to post this in the MS forum to get more suggestions from other 360 owners.
http://vgchartz.com/forum/thread.php?id=14073
This thread might also help you out too :)
starcraft: "I and every PS3 fanboy alive are waiting for Versus more than FFXIII.
Me since the games were revealed, the fanboys since E3." 
Skeeuk: "playstation 3 is the ultimate in gaming acceleration"
