Shopping in Vienna is possible nearly in any part of the city.
Of course, there are main shopping streets such as “Kärntnerstraße”, “Mariahilfer Straße”, “Landstraßer Hauptstraße”, “Favoritenstraße”, „Meidlinger Hauptstraße”, etc.
A good way to find shops is by having a look at the yellow pages. Shopping centres are located at the main shopping streets or on the outskirts, e.g. the “Millenium City” (U6 Handelskai), “Gasometer” (U3 Gasometer), and the “Donauzentrum” (U1 Kagran).
A bit outside Vienna, you find the “Shopping City Süd (SCS) – you can get there with a local train (“Badner Bahn”). There's also IKEA in Vienna, at the SCS and at the “Südosttangente” - a main road connecting the north with the south of the city (24A Zwerchäckerweg).
Unfortunately, there are also some pickpockets around in the city, especially near the major markets like “Naschmarkt" or "Brunnenmarkt". Please take care of your backpacks and purses.