I'd run it so that it runs the length of the largest expanse you'll see at once--side to side across the LR/kitchen. It's no sin (except maybe on this forum) to change directions at room entries if you like. I don't think there is a wrong answer, so do what you like.

We just replaced the Coretec flooring in our great room with solid hardwood, and changed direction. Our layout is similar, with two hallways and the kitchen on one side. See which you like better.