For people who like simple cookies, tender snickerdoodles are better than the fanciest decorated cookie. They are all about sugar and spice, but if you like vanilla, add a teaspoon to the dough. This recipe makes a lot of cookies, so have designated recipients before you start baking.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt. In a large bowl, beat 1 ½ cups of the sugar and the butter with an electric mixer set on high speed until combined, about 1 minute. One at a time, beat in the eggs. With the mixer on low speed, mix in the flour mixture, just until combined. Cover the bowl with plastic wrap and refrigerate until the dough is chilled enough to handle easily, at least 2 hours, or up to 1 day.
Position the oven racks in the top third and center of the oven and preheat the oven to 350 degrees. Line 2 large rimmed baking sheets with parchment paper.
Using about 2 tablespoons for each cookie, roll the dough into balls. In a small bowl, mix together then remaining ¼ cup sugar and the cinnamon. A few at a time, roll the balls in the cinnamon sugar to coat and place in a baking dish. Then, arrange the balls of dough 2 inches apart on the prepared baking sheets. Refrigerate the remaining dough balls while you bake the first batch.
Bake, switching the positions of the baking sheets from top to bottom and front to back halfway through baking, until the cookies are lightly browned around the edges, about 12 minutes. The cookies should be soft; don't overbake. Let cool on the baking sheet for 5 minutes. Transfer to a wire cooling rack and let cool completely. Repeat with the remaining dough balls, using cooled baking sheets.