The FamilySearch database entitled Austria, Vienna Population Cards, 1850-1896 documented local residents and travelers living in Vienna for the time period of 1850 through 1896, with the original documents being housed in the Wiener Stadt- und Landesarchiv (Vienna City and Provincial Archives). These records have been preserved on microfilm through the LDS and consists of 3,173 microfilm, which can be reviewed here in the microfilm catalog. Although there lacks to be a complete index for this collection, a great deal has already been indexed and provided online. I personally found the search form for this database to be rather limiting, with it not providing an option to search for an individual's place of birth, so I figured out a work-around.
Running a basic search for Hungary in the "Any Place" section on FamilySearch pulls back over 31 million results. We can restrict these results to specific Collections through the filter options on the bottom left of the search tools, which is shown in the red square to the left. Clicking on Collections brings up many categories of records, including 'Birth, Marriage, & Death', 'Census & Lists', 'Migration & Naturalization', 'Military', 'Other', and 'Probate & Court'. Scroll down to the second from last category entitled 'Other' and chose Austria, Vienna Population Cards, 1850-1896, with over 10,000 results. From here you can narrow the search down even further to your specific surnames and localities of interest, but be forewarned that Hungarian localities may likely be spelled in their German equivalent. One such example is Raab, or Rab, which is Győr in Hungarian. Unfortunately, digitized images of the content is not viewable through the index, so ordering of the microfilm is still necessary.
I have retrieved a copy of one of the documents to highlight important information that is contained in these records. This specific example is for an "Elek v. Eördögh", whose surname was likely Eördöghi/Eördöghy in Hungarian, that was residing in Vienna's district XVIII at Währingerstrasse 113 number 2. It states that he was born in Miskolcz Ungarn (Hungary in German), was a citizen of Maglod Ungarn, was born on 03 August 1863, was of the Evangelical faith (Augsburg Confession Evangelical), and that his wife was Etelka in Ungarn.
Other countries apart from Hungary can also be found in these indexes, including Romania (Rumänien) and Slovakia (Slowakel or Tschechoslowakei).