There is a lot of jazz in Vienna, but please note that the live activity dies down somewhat over the summer.
As far as I am concerned, the best jazz club in Vienna is Porgy & Bess. Excellent sound and a wide range of world-class acts. Here is the program: https://www.porgy.at/en/events/upcoming .
Jazzland is an old-style club for solid mainstream jazz: https://www.jazzland.at/e_index.htm
There is a nice club called Zwe. I was there just a couple of times. Good atmosphere, jam session type of place: https://www.zwe.cc/
Cafe Celeste is a no-frills underground place with often excellent free Improvisation jams (on Mondays, mostly): https://www.celeste.co.at/
There are many Viennese micro-labels, and this one is particularly excellent and criminally poorly distributed: Handsemmel (https://www.crackedanegg.com/handsemmel-records/) - just 11 releases in as many years, but each one is really high-quality stuff.
Jazzwerkstatt Wien (https://jazzwerkstatt-records.myshopify.com/collections/catalogue) releases a lot of interesting music, but it is all streamable / bandcampabale. This one is a sleeper classic, for example:
Enjoy Vienna, it's a great city - for music and much else!