Try dishcloth-type cotton (Sugar and Cream, Peaches & Creme, Lion Cotton, etc.) DOUBLED. Then pick a pattern from a stitch pattern dictionary and knit to size. You'll have thick, sturdy, washable placemats.
If you want to work with two colors, try the ball band dishcloth pattern from Peaches & Creme (it's also in the Mason-Dixon book), or any slip-stitch pattern.
Make swatches first and use them for potholders!