If I start in the middle, I will have to cut tile for both sides. I think I should start in the upper right corner, but my neighbor seems to think it will look out of balance.
Start in the exact center. This is where most people's focus will be and so you want to make sure it is centered properly. You'll have to cut the tiles to fit against the walls, but not many people will notice that.
When laying tiles always start with perfectly orthogonal lines intersecting in the center of your space. That's where you begin laying the tiles. The smaller the space, the more any imperfection will show.
Start in the middle. That's where the eye naturally strays. The edges, or corners will blend in. Yes, you may have to trim the pieces on the edges, but, it will be balanced from the center out. Good Luck!
Of course you start in the middle...but then again there are two ways of starting in the middle. Measure the space. Measure the tile and add the thickness of the future grout line. When you expect to cut the tile, and one always expects to cut the tile, you want to make sure that if you in fact begin with a GROUT LINE down the middle, you will have tiles of at least 1/2 the size down the sides. You don't want slivers of cut tile because your tile almost made it to the walls. So you may want a whole tile centered in the entry rather than the grout line. You can always lay the tiles out and see how it will look. Generally you do not want to use a wall as a straight edge, because usually they are neither straight nor parallel, nor perpendicular to other lines. Cutting a tile ever so slightly over a short distance will hide the building's flaws. Over a long distance it might become noticable. When you lay the tile out and you can decide where to end it rather than it automatically ending at a wall or something, you could start a nearly whole or whole tile at the door. Again you don't want a sliver of tile anywhere. If your tile is ceramic and has a stone pattern, be sure to orient them differently so as to minimize the repetitiveness. Never start in a corner.