"The Curtains of Night" is one of my family's favourites and has been my closing song for as long as I can remember.
Has become more poignant in recent years as some gigs I only do once or twice a year & each time I return it seems that someone else has moved on.
The upside, their children bring new spouses, kids & in-laws so the audience evolves.
"Four Strong Winds" is another which is usually sung toward the end of the evening.
If your question was really about songs I do rather than the last songs .... I'd be Traditional with just a few "Nancy Spain" type modern songs thrown in.