The post-WW1 era was as you say an era of massive change in Austria in general and Vienna in particular. There had been attempts in late October 1918 by the last emperor, Karl, to turn the Empire into a looser confederation but by then things were a bit far gone with Czechoslovakia and Yugoslavia beginning to coalesce and Hungary undergoing a revolution.
On 12 November 1918 the "Republic of German-Austria" (Deutsch-Österreich) was proclaimed on the Parliament steps, and two days later it applied for a union with Germany - "Austria" had always been a nebulous concept rather than an actual national identity and with the end of Austria-Hungary and Woodrow Wilson talking a lot about "self-determination", there was a feeling among the German-speaking deputies of the old Parliament that they didn't think a small rump Austria had a future as an independent country.
The union with Germany was forbidden by the allies - in general, the principle of "self-determination" only really applied to people in Eastern Europe previously occupied by Germany, Austria-Hungary, Turkey and Russia and not, for example, to the colonies of the victors or the desires of the losers. German-speaking minorities thus ended up being included in some of the new countries created. The "Republic of German-Austria" and the new Czechoslovak government, for instance, both claimed the Sudetenland, a majority German-speaking area within the old boundaries of the Kingdom of Bohemia, which is what the Czechs were using as the basis of their border claims. The peacemakers in Paris decided in favour of the Czechs. This would come back to bite the Czechs and ultimately Europe on the collective ass in 1938, but that's another story.
The Treaty of St-Germain-en-Laye, Austria's version of the Versailles treaty (tellingly, Hungary had its own separate one, the treaty of Trianon), officially ended this odd Habsburg rump state and created the new First Austrian Republic, and the new country was divided into a number of federal states. The problem was that one of them, the old feudal state of "Austria Under the Enns" - modern Lower Austria - contained fully half the population, much of it concentrated in Vienna. So, Vienna became its own federal state (though it remained also the capital of Lower Austria until that funciton was moved to St. Pölten in 1986).
The Mayor of Vienna thus ended up with the same political power as the head of, say, the Tirol, or the new state of Burgenland (from 1921 when the last territorial transfer with Hungary took place).
While all this chopping and changing of lands and borders was going on, there was a massive population exchange going on as those German-speakers who really didn't want to live under Czech, or Hungarian, or Yugoslav (etc) rule upped sticks and headed for Austria, while those Czechs, Hungarians and Yugoslavs (etc) who wanted to live in their own ethno-state left.
All of which left Vienna a shadow of its former multi-cultural self, for sure, but still full of immigrants, newcomers and people who only really had their language in common with their neighbours - imagine coming to Vienna from some little German-speaking village in modern Ukraine. Meanwhile, much of the traditional Viennese bourgeousie middle-class had been ruined by the war, having sunk their savings into now-worthless war bonds and been disproportionately affected by the failures of banks.
So while most of Austria consistently voted in a series of conservative-religious-right coalitions, Vienna did the complete opposite and went very heavily socialist. Between 1919 and the outbreak of the Austrian Civil War in 1934, Vienna was nicknamed "Red Vienna" (Rotes Wien) and adopted some of the most groundbreaking social policies for the time seen anywhere in Europe. Probably the most famous, and certainly the most lasting today were the public housing projects built to try and clear the slums and stop the spread of diseases like the Spanish Flu by giving people decent places to live.
The poster-child for this, and for the concept of Rotes Wien in general is the Karl-Marx-Hof, the longest single residential building in the world at just over 1km in length, but there were thousands of other smaller projects all over the city. Walk anywhere in Vienna today and it won't be long before you see red plastic lettering announcing "Erbaut von der Gemeinde Wien" (built by the City of Vienna) and a date sometime in the 1920s and 30s.
Vienna's public transport infrastructure remains one of the best in the world, and although much was built during the Imperial era, it was again a priority of Rotes Wien to run and expand the network of trams and buses, as well as taking into public ownership the elevated Stadtbahn railway that today forms the basis of U-Bahn line U6 and part of U4.
In the same way as the city of Washington, D.C. has seen itself recently at loggerheads with the President, Vienna became something of a centre of intellectual opposition to the largely bourgeois, conservative government. Where in the Belle-Epoque era before WW1 Vienna was a centre of arts and theatre, music and philosophy, "Red Vienna" continued to attract intellectual figures such as Schönberg, Schopenhauer, Wittgenstein and so on.
Not to say that it was all sunshine and roses, of course. Vienna continued to have a large Jewish community until the Nazi era, some of whom were very visible immigrants from points east, who tended to be both poorer and more Orthodox, wearing ringlets and yarmulkes and speaking Yiddish - and there was still plenty of antisemitism to go around. Moreover, as the orthodox Jews tended to vote for specifically Jewish parties and fought the Social Democrats for votes, official policy often didn't look too kindly on them either.
All these internal divisions within Vienna and between Vienna and the rest of Austria came crashing down with the beginning of the Austrian Civil War in 1934. With Europe increasinly polarising into "Facists v Marxists", a massive concrete construction called the "Karl Marx Hof" was an obvious target for accusations that it was built as a secret Marxist fortress, that its design was deliberately done to make it hard to assault. One of the key moments in the Austrian Civil War was when the government forces actually shelled the KMH.
Anyway, we're getting off topic and somebody will be along wanting sources in a moment, so here's some. Unfortunately most of that came from my own memory, visits to museums and so on when I lived out there, and it doesn't seem to be well written-about in English. So here are some places you can find out more.
The Habsburg Empire by Pieter M. Judson, on the messy end of said Empire
The Peacemakers by Margaret MacMillan, on the machinations of the post-WW1 peace converences in Paris.
The Vanquished: Why the First World War Failed to End 1917-23 by Robert Gerwarth on the various ongoing conflicts that cover the "end" of the war.
*The Architecture of Red Vienna, 1919-34" by Eve Blau. This is a rather expensive hardback coffee-table picture book I remember from my local library in Austria.
I have also had recommended, but haven't actually read myself, Red Vienna: Experiment in Working-Class Culture 1919-1934 by Baylis and Gruber. Now I've remembered about it, I really must see if I can get a copy.
