This is an excellent question with many options. If I were making a memory box for Scout, I'd think of memories that mattered deeply to Scout in the novel. For instance, you could include a blanket to represent the blanket that was put on her shoulders (by Boo Radley) when the fire broke out at Miss Maudie's house. This was one of Boo's early acts of kindness toward the children.
Another idea would be to include some items that the children found in the tree hole (where Boo Radley left gifts for the Finch kids). Some of these gifts included sticks of gum, the carved figures of soap (in the shape of Jem and Scout), and a spelling bee medal. These gifts (as well as the blanket mentioned previously) revealed to Scout that Boo Radley was not a monster.
Another item that Scout seemed to value in the novel was the gun that Atticus gave to Scout (as well as a gun for Jem) for Christmas; it might symbolize the important life lesson that she learned about not harming innocent creatures after receiving this gift. A gun could also represent the time her father shot the dangerous rabid dog.
Finally, I might include a baton, to represent the baton that Jem purchased Scout with money he received for his 12th birthday. After buying this gift for Scout, Jem ended up getting very angry with Mrs. Dubose, and he attacked her flowers with the baton. Atticus made Jem apologize to Mrs. Dubose; Jem also ended up having to read to her in repayment for his crime. Scout learned important lessons from watching her brother make a mistake and repent from his wrongdoing.