If you are designing a diner style retro kitchen, laundry room or even basement, you might want to consider this black-and-white floor tile in resilient sheet vinyl from Mannington, Armstrong, or Tarkett. Above: Armstrong.
In my experience, sheet vinyl is low cost and super easy to keep clean. 9″ squares, if you can find them, would have been the size typically used in mid century homes. 12″ squares are more common today. And Armstrong has both solid and marbleized squares to choose from. You also can achieve the black and white checkerboard look using 12″ x 12″ VCT tiles, which are going to require regular polishing and buffing… in linoleum from Forbo/Marmoleum or Armstrong… updated 2021: now there are 9″ tiles too! … or by using ceramic tile, which will be harder under foot.