what are the two places Gene wanted to visit?

Gene is visiting these two "fearful sites" as an adult. They hold bad memories for him. The tree is the place from which Phineas fell, as an adult he sees it is "weary from age, enfeebled, dry." Because of this, Gene comes to understand that, "Nothing endures, not a tree, not love, not even a death by violence." Seeing the tree again gives Gene a sense of peace, and he finds himself changed by the experience.

The marble stairway is located outside the Assembly Hall in the First Academy building. The stairway serves as the setting for the Gene's trial (did he, or did he not, jostle the tree limb on purpose?), and also the place where Finny "clumsily fell down the white marble stairs," as he angrily walked away.