There are a wide variety of sources you may find among family and home
documents. The list is too long to repeat here, and may be found in
any number of beginner books about starting genealogical research. Just
remember, any document about you that you may have had in your possession
during your lifetime, represents a similar document about your immigrant
ancestor that may have ended up with your family archivist. This includes
family Bibles, passports, naturalization certificates, insurance papers,
school records, church certificates and a host of others. For most 20th
century immigrants, many such papers will mention their home town in
the old country.
However, the reason these records are so much better for recent immigrants
than for earlier ones stems from two situations. First, the more recently
documents were created, the less likely that they have been lost or
destroyed. Second, the more time that has elapsed since an immigrant
arrived with such records, the more descendants have been born and have
migrated to various places in the new country. For any 18th century
immigrant, these records may exist, but you may not have any way of
locating where they are. Of course, some, such as photographs, can only
exist since the mid- to late-19th century.