Into the Mystic sounds like a great one.
Without putting too much thinking into it:
Cold Cold Ground (Tom Waits)
He Went to Paris (Jimmy Buffet)
Try to Remember (from The Fantastyks)
One Bourbon, One Scotch, and One Beer (George Thorogood)
Summertime (from Porgy and Bess)
My dad requested "When the Saints Go Marching In" and that seemed like a good one too.