Which way do you run hardwood flooring to make the room look bigger?
Rule of thumb is that hardwood is installed parallel to the longest wall to create the largest feel.  Since your room is almost square, I would be tempted to install it parallel to the door or entry. The other consideration is how much subflooring is under the new floor and what kind of floor you are installing. If you are going to install 3/4" nail down over a single 3/4" subfloor, I would run it perpendicular to the floor joists and be sure to nail into the joists. If you are  using a staple down, glue down or click lock, the choice is more arbitrary. Yet another factor is the subfloor thickness and clearance to doors and adjoining floors. If you are using a thinner flooring, You should have the basic 3/4" sheathing with at least 3/8" subfloor installed over the 3/4". Paper between all wood layers to prevent squeaking.