None of the EGYED immigrants who arrived through Eliis Island were from Vienna, Austria, so the chances of her being born in that town or her anecstors being from Vienna, Austria are slim to none. :) That information was noted somewhere probably by mistake because she was from Austria(-Hungary).
http://www.jewishgen.org/databases/EIDB/engine/gold.php?uid=...EGYED ethnic Hungarian family comes from all over the former Austria-Hungary - places that are in Croatia, Serbia, Hungary, Romania, Slovakia today.
You should concentrate your research on looking for any document that will give you a more accurate place of birth for her or last residence before emigrating for either her or her brother. His name would have originally been Mihály Egyed. Are there any naturalisation documents, ship manifests, death or burial records you could obtain? Sometimes in the marriage records of the children the parish of origin of the parents of bride and groom was noted, so look for scans of originals of such records, not the transcripts.
Also you need to establish and confirm in original period records the original surname of her husband Wally/Valle, that could narrow down the region where you need to be looking for her origin as well.
Availability of records that you will need after you establish where she was from varies:
-present day Hungary is partially available for free and can be researched either as indexed records or original images:
https://familysearch.org/search/collection/results?count=75&...https://familysearch.org/search/collection/list?page=1&c...- present day Croatia is partially available for free, original records, no index:
https://familysearch.org/search/image/index#uri=https://fami... - present day north Serbia and south Hungary for the locations where EGYED family lived is fully available original records but for a subscription fee, with some of the handwritten church indexes of records available for free:
https://www.facebook.com/rodoslovlje/photos/pb.198903800419....- present day Romania: a small selection of vital records and indexes is available but only for registered users of archive networks and with special academic permits. In most cases you need to either research locally in church and state archives there by hiring someone or try and find information from secondary sources.
- ZlaticaBeca already gave you information on possible places of origin and will be able to help more with records if your EGYED ancestors were from present day Slovakia.
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"Rodoslovlje" Serbian Genealogy Society
www.rodoslovlje.com