After Aragorn's passing, Arwen Undómiel departed Minas Tirith and returned to the desolate realm of Lothlórien, where she eventually laid down her life.
Arwen's Final Journey
Upon the death of King Elessar (Aragorn), Arwen chose to leave the splendor of Minas Tirith. Her journey led her back to the ancient Elven woods of Lothlórien, a place that held deep significance for her and her kin, but which by then was largely abandoned.
Her Last Days in Lothlórien
Arwen resided in Lothlórien for a period following Aragorn's death. It was there, in the year 121 of the Fourth Age (Fo. A. 121), that she eventually gave up her immortal life. Her final resting place was at Cerin Amroth within Lothlórien, a green hill where she and Aragorn had once pledged their love.
Significance of Her Choice
Arwen's decision to forgo immortality for love meant that she would share the fate of Men, including death. Her final journey to Cerin Amroth, a place of beauty and remembrance, symbolizes the completion of her choice and the sorrowful culmination of her long life and deep love for Aragorn.