My great-grandmother Esther Takats came from Budapest. She was born in 1889. Her maiden name I am not sure what which variation of Varady/Varadi I only know that she was related to a Sandor Varadi (I think he was maybe an uncle) who wrote her from Budapest. She married Stephen Takats also born in 1889 whose last name was changed from perhaps Takach (?). Both Eszter & Istvan have many variations so trying to find anything has been difficult with both families. Did you have any luck with your research?