Schedule delivery plugin wanted

My business will deliver locally. My city is broken into quadrants, N, NE, E, SW etc. I will deliver to specific quadrants depending on the day (Monday deliver to N,NE,E, Tuesday SW,S,SE etc.)
I am looking for a plugin that will allow me to have a drop down where the customer can choose which delivery day based on their quadrant.
I found this example on another website in a different city. As my city is not very big, I do not need zip codes.
The website I found that offered this feature is:
I do not believe it is a wordpress site. I am hoping someone can offer a plugin or woocommerce extension which can accomplish this.
Thanks!

The page I need help with: [log in to see the link]