I could have titled this, "Uses for a Fat Quarter When You Travel", but I thought better of it because the point is to stop at quilt shop. Lots of them.
To start with, do not under any circumstances leave home with a fat quarter loose in your car. Check out locations of quilt shops along your route.
Set out with your hair combed and a serene smile upon your face. Once you are at least an hour from home, begin fanning yourself and sighing softly. Adjust the visor frequently. Remark how your arm is getting quite the "traveler's tan". Attempt to shade your legs with a tissue. Run your fingers through your hair so that it stands up wildly.
Say something like, "Wow! A fat quarter would come in really handy to shade my ______ (arm, leg, etc.). " Dab at your forehead and look droopy.
Then, a few minutes later add, "Look at that! There's a quilt shop right off of this exit. I bet they have fat quarters!"
After successfully stopping and procuring at least a fat quarter, begin looking for other uses fat quarters in the car. Only share one at a time as needed, about 10 miles before the next quilt shop.
Emergency water towel
Cover travel mugs to keep the sun off
Cover shiny objects reflecting sunlight into your eyes
Hang in window for a shade
Extra layer for warmth
Inexpensive hostess gifts
Picture borrowed from The Spruce. Please visit there for more information on fat quarters.