After walking a mile up the road following signs for a SPAR supermarket so I could buy beer for my hotel room, I found the Cafe Ritter. I pulled the attached picture from the web, but it looks correct. There is more than one Cafe Rittner in Wien. The outside of the cafe looked faded, but the inside looked authentic.
I had a coffee and an Apfelstrudel. I like the way you get a glass of water with your coffee in Austria. I have found that if I drink more than 5 or 6 cups of tea before midday, I can't drink anymore, unless I have a glass of water.