With a checkered floor next door, the rug has to be the calm one — any pattern in it will fight the checker and that's the chaotic feeling you're getting. Go solid or near-solid, and let texture do the work instead of pattern: a low-pile wool or a subtle tone-on-tone weave. Pull the rug color from the quieter tone in your checkerboard (usually the cream/off-white square) so the two floors read as one palette instead of two competing ones. Size matters most in an open loft: big enough that the front legs of the sofa and chairs all sit on it — the rug is what draws the line between living room and kitchen when there's no wall. And keep the border plain, no busy edge. If you do want a little pattern later, add it in pillows or a throw, where it's easy to swap out.