Best places in Vienna downtown to buy a cheap SIM card?

If it is just about data, don't panic. Free Wifi is nearly everywhere available in Vienna, along major streets, in touristic areas, in all restaurants and cafés, in hotels, etc.

Vodaphone does not exist in Austria. A1 and T-Mobile are the two major players, but there is a plethora of offerings.
See a comparison here (set the sliders on the left according to your requirements):
https://www.tarife.at/wertkarte

Note - T-Mobile is now Magenta.

I’d recommend going to a Hofer supermarket (Aldi in the US) for a card and data. Or try an Interspar supermarket, the cards are just a few euro. By law you will need to register your SIM card usually through the internet.

Thanks for the leads. This is proving more difficult than I expected. To start with, substantially all of the shops that sell this kind of thing are closed in Vienna on Sundays.

Yup, all shops are closed on Sundays here.

There is an Interspar Pronto supermarket in Vienna's main train station, which is open on Sundays until 11pm. But I don't know whether they sell SIM cards.

I guess, if yor mobile phone is a modern one with eSIM capability, you can buy the eSIM online, because no physical SIM is required anymore.

But as said before, having free WiFi everywhere gives you the opportunity to make voice and video calls, to have access to your email, etc.

Thanks! I see there is a Hofer and an Interspar both within a 5 minute walk of my hotel.

Who is your US internet provider? The larger companies offer an international plan that is easy to use. We have Verizon and used their plan. It's $10.00 for 24 hours. If you don't connect for a few days, you won't be charged.

My U.S. cell provider is Verizon. But $10 per day is pretty outrageous rate. It's 10x more than you need to be paying. Now I realize that some people are fine with this, and won't have any issue with paying $10 per day, day after day. But if this is significant enough that you will try to avoid using it some days, in my opinion that is a problem.

The benefit of having data is being able to use Google Maps throughout the day every day, getting pedestrian directions and transit directions, and getting the full range of info for restaurants and the like, This is how many of the locals get around in their cities, and we the usefulness of this cannot be overstated. Once you start using this, you will never go back.

By the way, I went around to multiple places yesterday. Most of the SIM cards sold in Vienna are only good for use in Austria. They have very onerous roaming terms for outside of Austria. And Magenta (what T-Mobile is branded here) was just as useless as most of the others. They told me you could only get decent roaming outside of Austria if you signed a 2-year contract.

But I did find a good option. Drei (that is their name--the German word for three). They have affordable pay-as-you go SIM cards with good roaming terms. For 30 Euros I get 19.5 GB of data that I can use outside of Austria in the next 30 days. There is a Drei right across from the main door to the St. Stephens Cathedral. That is where I bought my SIM.

But generally speaking, I think Vienna is not a good place to get SIM cards. There are better, more affordable choices in London. And you can also buy SIM cards online that are shipped to you before you leave. (And if your phone supports eSIM than you have even more options.)

One thing to be careful about: To purchase certain items abroad using your credit card the purchase won't go through unless you get a code on your phone from the credit card's verification service and enter that on the web site. Where I see this coming up is on event/museum tickets and also train tickets and the like. And of course the credit card company uses the phone number on file with them--and so if you've swapped out your SIM this won't work.

One work around: Set up a Google Voice number and use that instead. And A Google Voice number is great for traveling overseas anyway.

But generally speaking, I think Vienna is not a good place to get SIM cards.

The problem is the huge number of choices you have. There are 30+ companies offering SIM cards in various variants. Even when using a comparison portal it is difficult to find the best option.

The benefit of having data is being able to use Google Maps throughout the day every day, getting pedestrian directions and transit directions, and ...

As I noted before, Vienna has a plethora of free WiFi hotspots. Using WiFi gives you the opportunity not to consume your data allowance from the SIM card. Set your mobile phone accordingly, i.e. that you get a notification whenever a WiFi is available.