I have a book called Play Quilts: Creative Activity Quilts for Kids by Kristin Kolstad Addison. They don't have a car play mat but by looking at her examples it might help you decide on a design. I made my daughters a pirate ship quilt.

The nice thing (that you can't tell in the picture) is that the boat is usable - only the bottom is sewn down. So, we can put animals in the ark or mermaids or princesses (or pirates). Same for the boat house. And - the purple ribbon is a swing for the mermaids. Hmmm - the sun looks like he needs ironing.
Other activity quilts in the book are: an animal train, a sleepover picnic, a flight to the moon, and a farm. The animal train just has a piece of binding meandering along the quilt. I think the train cars are sewn down (on the bottom) because there are animals (that she also tells you how to sew) that can go in and out of the train cars.
It was actually a really quick quilt to put together (size approx 53 x 40). I keep meaning to do another from the book but haven't yet.
Have fun, Beth