Whisk sugar and cinnamon together in a pie plate or shallow dish.
For the Snickerdoodles
Preheat oven to 375 degrees (F).
Whisk together flour, salt, baking soda, and cream of tartar.
Cream together butter and sugar until light and fluffy, about 2 minutes.
Add eggs, one at a time, beating well between each addition.
Add milk and vanilla extract, beat until combined.
Slowly add dry ingredients into the creamed mixture.
Mix until everything just comes together, scraping down the bowl as needed.
Check the consistency of the dough, you may have to add few tablespoons more flour. You should be able to touch it without it sticking too much to your fingers.
Form dough into 1-inch balls
Flatten the caramel until it is the size of a quarter, cut in half if necessary (see note).
Place the caramel into the center of one ball and then place another ball on top of the caramel so it's completely covered. It should be slightly flat and disc shaped.
Roll the dough in cinnamon sugar mixture.
Place 12 discs of dough on each cookie sheet, baking on the middle rack of the oven, one at a time.
Bake for 8-12 minutes until the edges are set and the very middle still looks slightly under baked.
Notes
If you use the square, individually wrapped caramels (like Kraft or Brachs), you'll need to cut them in half. Otherwise, they will be too thick and won't melt properly. If you want to use the caramel bits in the baking section, use about 3 per cookie.