I went in January with a group of friends for my thirtieth, we stayed right by the palace, it was snowing and so cosy and pretty.
I would recommend visiting the library, there was an Austrian parade going on, lots of people in traditional costume, horse and carriages, interesting things to see. We also climbed the cathedral and visited a sky bar near it where we had the most amazing apple strudel.
We also went to the Ritz for drinks one night but were shocked at how thick the cigarette smoke is everywhere. Just a little warning, I’m a non-fussed ex smoker and there were smokers in our group, but even for us it was a bit much. They put heavy curtains over the doors everywhere to keep the heat in but it does make the bars in to real smoke boxes.
We had a delicious evening meal at Paul not far from the Ritz.
We discovered they party very hard there when some businessmen in our hotel invited us in to their work’s party, they were still going strong until about 6am in ballgowns and tuxedos, then all down at breakfast by 10!
It was absolutely lovely. Trams were easy to use and get around on. Everything easy to find (some of us know basic German which made it easy to translate most things.)
Enjoy your trip! You’ve made me now look in to doing a German market next year :)