Very nice scarf, and what a great color!
You could finish with a picot bind-off. Ending on a RS row, this will necessitate you picking up stitches on the three remaining sides, with extra stitches for each corner, directions:
Begin with an even number of stitches (RS) Bind off 2 stitches, slip stitch back to LH needle, and using the cable cast on method, cast on 3 stitches, bind off 5 stitches repeat from to.
I love jinx's idea of tassels, also. These could be worked on all sides of the scarf, if you like, placed at intervals of your choosing.