This is an interesting question because it leaves so much to the imagination. Shakespeare's stage directions are purposefully always vague, so to have the freedom to design the final image(s) that the audience would see in a production of Othello is quite a treat!

Act 5 of Othello is highly dramatic, so the final moments of the play should echo that drama. What directing the play would give is the opportunity to refocus the play on the two characters who are the most key to the progression of the plot as a whole: Othello and Iago. Although Lodovico is technically the last person to speak in the play, his role overall is extremely minor. Thus, I might have him narrate while walking past the other characters with lights on those other characters as he speaks. Firstly, he speaks to Iago. Then, he tells Gratiano to take care of Othello's things. Then, he appoints Cassio as governor and permits him to punish Iago in whatever way he sees fit. Then, he says that he will return to Venice with the story of what occurred, specifically in reference to Othello and Desdemona.

A prop that would allow blood to run from the bed where Othello and Desdemona are laying onto the floor surrounding them would be an extremely powerful image with which to end. Although music could be used effectively here, I believe that silence would send an air of solemnity more effectively, thus demonstrating the sheer waste of life that took place. I would leave the light on them for the last few moments while Lodovico exited following his monologue. Then, I would have Gratiano follow since they traveled together. I would choose to leave Cassio and Iago onstage until the curtains closed to emphasize their ties with the dead couple.