Vienna is a very cosmopolitan and colorful city. I visited the city many times and every time I was charmed by the diversity of what the city offered. In every season, there are some specific events going on, so that tourist can see the beauty of the city.
I would say that winter and summer the best time for visiting is. In the winter you have to see the Christmas markets and drink the Glüwein (the warm wine is called this way) or taste the sweets. You can also buy little Christmas ornaments, or presents for family and friends. It´s like you are in a colorful fairytale.
Summer is great cause it is not too hot and you can discover the little places and things that make the town special – great architecture, impressing parks, the Belvedere and the Zoo. It is a very pleasant and safe city to visit. It is not the most expensive one to visit, but not too cheap, so you should prepare some hundred euros for a week here.
In any season I would recommend a walk in the Ring, where you will see all the big and important buildings of the city, get a sense of the new and old.
You should definitely visit the Schloß Schönbrunn (Schönbrunn castle), the museums Albertina and Leopold, the Kalhenberg (it is a hill from where you can see all the city) and for shopping the Mariahilferstrasse and the Donauzentrum.