One of my favorite things to do in a new city is to explore the supermarkets and gourmet grocery stores. There are a few in Vienna that are worth a visit - I thought I would give an overview.
Gourmet Grocery Stores:
Meinl am Graben - This is the OG gourmet grocery store in Vienna. Located at the intersection of the Graben and Kohlmarkt in the First District, Meinl has two floors of gorgeous food, including ready to eat items and a dairy case of your dreams. But I think that the chocolate section is the real highlight, particularly during Easter and Christmas. For a great view of the Graben, go upstairs and look out the windows next to the bakery.
Billa Corso at Hoher Markt - While there are several Billa Corso (the high end version of the ubiquitious Billa chain) around the city, the primo location is here at Hoher Markt next to the notable Ankeruhr. Several levels in this shop include great options on the go as well as Billa standards. (Note - the Billa Corso at Neuer Markt, also in the city center and also very nice, is open on Sundays).
Interspar am Schottentor - This is the new kid on the block, the gourmet version of the Spar chain located in an old bank. The setting is stunning. While this location offers typical Spar products, you will also find good food to go as well as unique items.
Regular Grocery Stores:
Since I'm on the topic, I can also give some normal grocery store insight. In Vienna, you will find a Billa or a Spar on nearly every corner of the city. Although these can be of varying sizes, the will offer the same products essentially. As mentioned above, larger Billas are called Billa Corso and Spar has Eurospar (a bit bigger) and Interspar (quite big, carrying household items as well). Any of these are worth a browse.
You can also find Hofer (known as Aldi in the US and elsewhere in Europe) and Lidl shops throughout the city. Hofer is known for having the best produce selections of all grocery stores.
And finally, you will see the very cheap PennyMarkt around town as well as large Turkish grocery chains like Etsan.
You might also spot a Mueller around town. Mueller has just about everything, including toys, high end make up, perfums and also food. Kind of fun to poke around.
Drug Stores:
This is a misleading title as drug stores, like Walgreens or CVS, in Austria do not sell drugs - not even over the counter meds. For any type of meds, you need to go to a pharmacy/Apotheke. The common "drug" stores in Austria are DM and BIPA. These shops sell a larger range of body care products, make up, cleaning supplies and some snacks. Locals really love DM and particularly their Balea range of products, which are cheap and good quality (make good gifts).
I hope this is useful!