We will be in Vienna in the middle of may and would like to experience a classical concert in this City of Music, preferably in one of the historical venues. Any recommendations? I am also curious about the expectations for dress. We pack lightly because we carry our belongings in backpacks and our clothing is usually casual, not what I would choose if going to a classical concert here. I am wondering in this tourist-filled city what the norm is.

Depends on your taste, but the organ concerts in St Stephen’s cathedral are as atmospheric as anyone could wish.

https://www.viennaticketoffice.com

May 6, 13 and 28 if any of those work for you.

Check the schedule of Musikverein to see if there is a concert performing in the Golden Hall (the large hall, not any of the smaller halls) that you like:
https://www.musikverein.at/