Start with when and where they died. If you haven't already I suggest getting their death certificates and obituaries. Also check with the church they were members of and cemetery they are buried in to see what they have in their records on them.
Death certificates should list their parents as might the obits. The obits might also list surviving siblings which can be quite helpful as well as the towns they were born in. The church and cemetery records might also have parents' names and towns of birth.