Vienna in December

The U4 subway takes you to Shoenbrunn. Dress warmly as there is a bit of walking involved.
There is a Christmas Market at Shoenbrunn and there are several others to chose from. Which one or ones you choose might be a function of where you are staying...Boats dock in the area of the Reichsbrucke...you can walk from there to U1.
I Iike this one https://weihnachten.altwiener-markt.at/
Not knowing what tours they are doing...you may be better of escaping. Shoenbrunn is always on my list of stops but it's not at the top. I love the museums and churches and the coffee shops.
Google is your friend. Anything you want to learn you will find.....https://www.austria.info/uk/things-to-do/skiing-and-winter/christmas-markets/christmas-markets-in-vienna

Depends where you dock.

Take the subway to Schonbrunn. Tour the interior and focus on the Christmas market there. It’s a good one for food. Have lunch at the market.

Take the subway (U4) to Karlsplatz and change to the U2 line getting off at Volkstheater. Walk to the Spittelberg market for shopping and a warm drink.

Take the U3 line to Stephansplatz. I suggest walking down the Graben then left onto Kohlmarkt. Turn left on Augustinerstasse to Kaerntnerstrasse. Wander some back streets to the cathedral. Have a coffee at Diglas or Alt Wien.

Depends where you dock. Take the subway to Schonbrunn.

The bigger river cruise ships are moored mostly near Reichsbrücke (Imperial bridge). Walk to the bridge and then a short distance downtown (i.e. away from the river), then you will see the entrance to the subway U1 (red line, stop Vorgartenstraße), go to stop Schwedenplatz, change there to U4 (green line) to Schönbrunn.

Thanks everyone, very helpful! Excited about this trip and any information to help make it more enjoyable is truly appreciated!

New development on our trip and I need help: My mom came home to her home being broken into and completely destroyed by vandals. She does not want to cancel the trip, so that being said; I want to make this a very relaxing trip full of pleasant memories. That means I need to look into as much ground transportation as I can and maybe have them scheduled before we leave. How are taxis, Uber, etc. in that area? I know it will be very cold, so we may have to make adjustments along the way. But I want all the stress to be on me and for her to feel none of it. She has enough right now.

Uber works well as long as you have wifi or an internet connection. This might be challenging for you. Taxis are around, but in Vienna you can only hail them from designated areas, which are not always convenient. Honestly, public transportation is really the easiest way to get around this city.

Uber works well as long as you have wifi or an internet connection.

In Vienna (free) WiFi (WLAN) hotspots are ubiquitous, public ones on the main streets, private ones in cafés and restaurants.
Check on the official map of the City of Vienna: https://www.wien.gv.at/stadtplan/en/
On the left side in the column "Show on the map" look for "Communication & business", click on the + sign to expand, put a check mark on "WLAN hotspot" and click on ">". Then you get public and private hotspots displayed on the map.

Taxis in Vienna are called by phone: +43 1 40100
All taxis have the same fare, just make sure that the meter is switched on.

Uber fares may vary depending on the weather and the demand.

I'll add to this - Vienna public transport is brilliant. I would expect having to deal with traffic in a taxi or other would be more stressful and take more time and cost more $$. While Schoenbrunn has its' appeal and you are looking for less stressful, there is so much to see "inside the ring" that won't require a lot of time in transport.