Personally, I would lay it in the direction you want in the bigger area, and keep that same direction everywhere. If you choose to change direction, you do not need "a trim strip or something to cover the transition" unless you have a terrible installer. I have changed direction in rooms vs hallways. You need to specially cut a groove in the first piece, or cut a special tongue piece to fit the 2 grooves together, depending on the direction you are installing. You just need to make the ends of one piece fit into the side of the next piece, and it takes a bit of conscious joinery. If your installer is some joe with no carpentry skills, he might just leave a gap and cover it with a speed bump. Don't let that guy install your floors. As for the direction of the joists, this was true back in the day, when you wouldn't have subfloor, or your subfloor would be in planks, so you'd have to be sure to run the planks in the opposite direction of whatever was underneath them. Is there a reason to keep doing that nowadays, when most people have 4x8 sheets of plywood as their subfloor?

If installing diagonal there is no need to be concerned with the floor joists if it's a solid 3/4" product. However if you reside in places that have different codes for subfloors(California for example) your subfloor may be suitable for any direction because of it's thickness. Longest dimension of the area is usually the best direction, but front to back in this case would look more appealing...if I'm looking at it right.

My living room, dining room, kitchen, and hallways have had hardwood floors since 2007. I'm finally getting around to taking out the ratty carpet in my three bedrooms and replacing with hardwood. It will all be unstained red oak. Although my existing floor is site-finished, I don't want to go through that again and I'm having prefinished for the bedrooms. I have a large sample and I think it will be fine, plus I'll be putting down area rugs. My question is what direction to run the new boards? The attached photo shows the hallway off which the three bedrooms open (#1, 2, 3). #4 is a bathroom with tile floor that isn't changing. The arrow points to the hallway that leads to the rest of the house (LR, DR, kitchen). The entire existing floor runs north/south as we look at it, and the only variance the hallway (arrow) which runs east/west. Is there a rule of thumb for the direction the boards run in the bedrooms? Each bedroom is somewhat square. There will be nothing run on the diagonal.

I really like that floor plan, by the way.