Good game for 369

If you're only playing a hour or 2 a week, probably not worth it to buy a retail game. Maybe a arcade game like Minecraft or something.

Well the 369 is not out, but for the 360 for I'd might suggest Mw3... Minecraft?

Definitely go for XBLA or XBLIG. There are so many nice little to medium sized games in every genre for little money. XBLIG is cluttered with low-quality stuff, though, so be sure to filter on rating and/or top-downloads. You will find good stuff there for just a few bucks, including very well done Minecraft Clones/Spin-Offs, 3d-Shooters, great RPGs and Platformers. IMO, the best choice if your goal is to have fun for little money.

XBLA has games with a higher pricetag than XBLIG ($5-$15), featuring games from AAA studios and might be a good choice for you, too.