What cities to visit in Austria?

I was thinking of visiting Austria the next month. I have not yet planned what exactly to see and explore in the country and, therefore, I would like to gain some information. What are your experiences? What cities to visit in Austria? Is there a particular city I should see? Thank you!

Be sure to visit Graz. It is the old town and it is thought that an early Roman settlement is beneath the city. It is the most beautiful historic centre in Europe. You may opt for Innsbruck also, the capital of Tyrol. It is popular among tourists for its ski resorts. There you can visit the Fürstenburg castle built in Innsbruck during the 15th century. And the Hofkirche, a Franciscan church dating from the 16th century. You don’t want to miss Salzburg, also. It hosts many internationally famous music and drama festivals every year.