Vienna is a seasonal town, and the best things to do are dependent on the time of your visit.
In Summer, you will have to contend with the crushes of tourism throughout Europe, and Vienna is no exception. Many restaurants and cafes will open their street-side seating and the city takes on a festive, outdoorsy atmosphere.
Fall offers the abundance of the harvest, less crowds and above-all, the tradition of Heurigen -- Austria's unique wine experience. Wineries are allowed to sell, for the period of about one month, their fresh wine and serve food. Think of it as brew pubs for the grape-oriented set.
Winter, prior to Christmas, is beautiful. Austrians begin celebrating Christmas with the Advent on December 6th, and even before. The city is decorated, peaceful and temperatures, while chilly, are not as bad as many would suspect. Hot spiced wine, roasted chestnuts and open air shopping spring up everywhere. After Christmas, forget it until Spring, unless you choose to celebrate New Year's (Sylvester) in Vienna. For this special occasion, the subways and streetcars run 24 hours and the city livens up.
Spring brings warmer temperatures and increased cultural opportunities.
Quick Tips:
Buy a pass for the subway/streetcar system at a Tobacco store (easily identified with yellow signs) and hit the road.
See the sights, but don't forget to do what Wieners do best and relax in a comfy cafe or beisl with a good beverage.
If you're in a party mode, Vienna boasts some of the best underground electronic music in the world as well as DJs and clubs to rival any city in quality, but not in number.
Austrians are very outdoorsy, so don't forget to visit some of the great city parks such as the Stadt Park and Donau Park.
Get into the outlying (2-8 especially, but you could go beyond) districts where the "real" people live and enjoy yourself.
Best Way To Get Around:
Vienna is consolidated enough that you can walk most anywhere and cover the historical sites/sights.
The city is organized into "rings" and districts (Bezirke). The First District is the center of the city and encompasses all of the area that was encircled by the city wall before it was removed. The next 8 districts (2-9) are arranced as slices of pie around the first district and form the first "ring" of Vienna. This pattern continues with the third ring. All addresses in Vienna begin with the district, then the address (for example: 9, Schubertgasse 36).
Once could easily stay within the First District, which is the oldest and has, consequently, the highest concentration of historically interesting cultural opportunites. But a lot of the best features of Vienna rest in the oulying districts immediately outside the city center.