Vienna is a gorgeous city. Within the Ringstrasse, most buildings have carvings and/or statues. We stayed in an apartment on the Danube Canal. The city is extremely walkable, and the public transportation is incredibly convenient and well run.
I highly recommend staying as long as you can. We stayed over a week (total time) and did not get to see everything.
Stay in Herr Heill's apartments (http://www.apartment.at/index_eng.php3/app/79). The picture on this website is accurate and doesn't even show how wonderful the apartment is. The apartment is huge. Herr Heill will meet you, show you the apartment, and tell you where supermarkets and sites are. The apartment is VERY quiet and extremely convenient to the old city.