I would lay them the same way between the rooms; have the length "pointing" to the best feature of the rooms, such as windows or fireplace.

You always want flooring to lay long in narrow areas such as halls and kitchens. Then carry the same orientation throughout the house. As stated above, definitely don't have it "pointing" at the most important feature. It needs to be running perpendicular. I'm always writing articles about house design. checkout my website and email me if you have any questions

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Get rectified tile not the cheap ones and before anything else make sure your floor is made stable enough for tile install as for the direction IMO they should be laid perpendiculat to floor joists just like real hardwood