Look on the Lion Brand website. They have loads of free patterns, and if you use the filters to narrow it down to 'afghans' (American for blanket
), you will see lots and lots of them. The kind you are looking for are 'sampler afghans' - one of my favourites is an aran one which has squares of pattern in a tile effect on a strip, which you can make as long as you like, and join together with as many as you like to get a blanket to your requirements.
If aran is not your thing, there are lots of others, or you could use the pattern as a guide to number of cast-on stitches/rows, and make your own design. Some rib, some moss stitch, some garter, some stocking stitch would be lovely, and very mindless and easy.
Oh, and Ravelry have patterns for knitted log cabin blankets.