SAVV and other companies have a screen that doubles as a rearview mirror. Pretty cool, except you need to check the laws in your vicinity for legality of that sort of thing like other's mentioned. Other common places for screens are headrests, mounted in the center of the dash, mounted on the inside of the sun visors.
Placing the Xbox could be tricky cause it's sort of bulky, but I bet you could fit it into your glove compartment with some cutting. Alternative is maybe slid under a seat on a sort of rolling tray if you've got clearance for it. Or you could figure out a way to mount it in the center console.
Of course, if you're feeling frisky you could always try taking it apart so you don't have that big ol' box to deal with

I don't recommend that particular one unless you're willing to break it, though.