MAKE DOUGH Combine flour, baking powder, and salt in bowl. With electric mixer on medium-high speed, beat cream cheese, butter, and sugar until smooth and creamy, about 2 minutes. Add eggs and vanilla and mix until incorporated. Reduce speed to low, add flour mixture, and mix until just combined. Refrigerate dough until firm, at least 30 minutes.
HEAT OVEN Adjust oven racks to upper-middle and lower-middle positions and heat oven to 350 degrees. Line 2 baking sheets with parchment paper. Place graham cracker crumbs in shallow dish.
ASSEMBLE COOKIES Roll dough into 1½-inch balls, then roll in crumbs. Place balls 2 inches apart on prepared baking sheets. Using tablespoon measure, make indentation in center of each ball. Place 3 cherries in each dimple. Bake until golden around edges, 12 to 14 minutes, switching and rotating sheets halfway through baking. Cool 5 minutes on sheets, then transfer to wire rack to cool completely. (Cookies can be stored in airtight container for 2 days.).