I may be the odd one out, but I an "either genuine hardwood or tile only" kind of guy, and after having genuine hardwood in a kitchen, I'll never live with that again!
Regardless, for directional preference, you can go either way, whichever suits you. E-W direction makes the plank lengths consistent with your described general travel path, but I expect there is equal travel time spent walking N-S as well while working or hanging our in the kitchen area. My personal instinct is the run the planks in the same direction as the longest dimension of the room (N-S in your case, by your sketch, anyway).
The question, though, is this... what is in the LR and the Hallway now? Planks, tile, carpet, etc.? If there is a pattern direction to either or both rooms, run your kitchen planks in a direction which compliments the other adjacent floor areas.