New York Passenger List - Mary Kelly born 1869 - Brexburn Scotland - aged 55 years
That's probably Broxburn, West Lothian - parish of Uphall.
There's a Stanrigg in the parish of New Monkland in Lanarkshire, and a birth of a David Kelly was registered in New Monkland in 1896.
There's a Kelly family in New Monkland in 1901 consisting of James, 39; Mary, 32; Margaret, 12; Jane, 10; Michael, 8; Mary, 4; David, 4; Helen, 2; and Maria, 0. Are they yours?
If so, any one of their birth certificates will tell you Mary's maiden surname and where and when she and James Kelly were married.