Wiki - Sightseeing
Please add any sightseeing tips here!
Basically, anything around and inside the Ringstraße, that is to say, the entire first district, is the typical old Vienna and also full of historic buildings.
If you see Schönbrunn Palace, also walk around the extensive gardens.
For things to see (besides the usual touristy stuff) I recommend renting a bike (better a proper one than a CitibikeWien) and cycle through Prater, Donauinsel and Lobau - Thomas Klausner (domm).