https://youtu.be/reSSvOnQEr8
Webster defines downtown as the lower part of a business center in a city or town.
From my recent visit, I would put downtown from 9th street to 2nd and all points east and west from I35 to Lamar.
I always preferred the naming of boroughs in NYC, Queens, Bronx, Brooklyn, Manhattan, and Staten Island. Midtown is the central portion of Manhattan, Downtown Manhattan is the southernmost part of Manhattan also known as Lower Manhattan. Upper Manhattan is the northern most region of Manhattan. Not sure the same designation can be applied to Austin, but by considering the densest parts of Austin's "downtown" this certainly could apply with the boundaries totally debatable. Perhaps 2nd to 7th or 8th, downtown, 8th or 9th to 12th midtown, and upper 12th to (I'm not sure where). Capitol District, SOCO District, East Austin District, Campus District just to throw out a few names. Yeah this is basically just rehashing previous discussions on this topic.