My daughter and I will be arriving in Vienna at 8:40AM and fly out at 10:30PM on December 23rd. As she is a horsewoman our first stop is a training session at the Spanish Riding School at 10AM. We will only have small carry-ons to facilitate getting into the city. We hope that we can make it there in time. We both can move very fast if necessary. We would like to visit some of the Christmas markets, one of the palaces, stop by the cathedral and eat.
Is this a reasonable plan? Anyone have any suggestions?
Sounds like a plan. Since you'll be in the center city, the downtown winter palace would be a good one to catch if you have time.
The Hofburg Imperial Apartments and Treasury.
Take the (red) RailJet train from the airport to the main train station (Wien Hauptbahnhof), leave there your luggage in a locker, go to the city center using the subway U1 (red line) to Stephansplatz. Same way back to the airport.
The RailJets depart every half an hour from the airport, i.e. 8:33am, 9:03am, 9:33am and so on.
If you can catch the train at 9:03am you can easily make to the Spanish Riding School at 10am. With a later train it is impossible.
As a fallback measure you can take the REX7 train at 9:11am, going to Wien Mitte (center train station), and go to the city center using the subway U3 (orange line) to Herrengasse. (Herrengasse subway stop is closer to the Spanish Riding School than Stephansplatz).
I don't know whether there are lockers at Wien Mitte train station, though.
Stop by Lugeck in Sonnenfelsgasse for a schnitzel lunch. It is very close to the cathedral and the statue of Gutenberg is right out the front. It's run by the same people as Figlmuller but has more modern decor.