A quick update, as it's been almost a year...
The Chegini on Kohlmarkt in the basement no longer exists. However, in its place they opened two new ones, both on Kohlmarkt. Both are kind of hidden inside courtyards but the street isn't that long so they shouldn't be very hard to find. One of them carries current stuff, the other is an archive with mostly things where you can see why nobody wanted them. But the prices are so low that it doesn't hurt to quickly stop by. Of course there's also the one on the corner of Plankengasse and Seilergasse, which tends to carry the stuff I like the most. They close at 6:15 and sometimes won't let you in at about 6.
Park is still around. They've opened an online store as well:
www.park-onlinestore.com.
Emis is also still around.
2006feb01 (dumbest name for a store ever) stopped carrying menswear. Thus mens Burberry Prorsum can no longer be bought in Vienna as far as I know.
Mühlbauer (the hat store) has a clothing store just across the street that stocks Vivienne Westwood, Petar Petrov, and others.
Song and the ACNE gallery are now in the same building.
Liska has about 500 different locations in Vienna and they stock a few nice things but unless you have an oligarch's inheritance, don't bother.
There's a small but nice women's Jil Sander store tucked away in a side street across from Stephansdom.
None of the bigger Austrian designers actually have their own stores in Vienna. Peter Pilotto is exclusive to PARK. Petar Petrov has his store in Paris, and only sells at Mühlbauer in Vienna (though he did have a sample sale a while ago). Wendy & Jim are still at PARK I think? etc... I guess the demand just isn't there.
The other stores already mentioned in this thread are mostly still around as well. Vienna is very resistant to change. To be honest it really shouldn't take more than a day (or two if you want to take it slow) to check out all that Vienna has to offer in terms of fashion.