Hello: My husband's family is from the Budapest area & I have found that his great grandmother was Erzsebet Barsi (1842-1885), from her birth record - her parents are Janos Barsi & Katalin Csontos. They were living in Baracska, Fejer, Hungary at the time of her birth. So far I have found 9 children for Janos & Katalin. If anyone knows about Katalin I would love to know more about her.
If you find a town for your family, be sure to check the LDS files to see if they have filmed church records there, you can then trace your family in Hungary & not guess or wonder.
Dianna